 Cool. Now we're live. Just confirming. Hi everyone, this is Chichou. Welcome to another live stream and today is May 24th, 2019 and this is a drop in math tutoring session number 29. Just making myself available for people that need a little mathematics help with mathematics, high school mathematics specifically. So that's what the stream is about today. I'm just setting everything up for my end here. That's what the stream is about today. Basically, in general, it's just an open discussion. We talk about whatever we want. But we try to gear it towards mathematics or physics or chemistry, sciences, basically academic stuff, mainly stuff related to high school. Obviously math centric. Aside from that, we're going to do this probably every week for the next month or so until the end of the school year. And then we're probably chill with it unless people really want to continue. And if people really want to continue with these live streams of just doing math sessions, we could definitely do. Maybe do them once every two weeks or once a month until summer's over and then we'll start back up again when the school year starts in my part of the world anyway. Okay. Thank you for hosting AeroCosmos. And usually we just wait a few minutes for people to pop in. If we're chatting about anything that is not math related or even math related, if you have any questions or any any concepts you want to talk about, just post them in chat and we'll make a little list and go through as much stuff as we can. I think what's going to happen slowly over the next few years, we're going to get more and more people popping in. So I think it might be a good idea to start making a list of some of the things we might want to talk about during these live streams and just take it from there. Right. And of course this, we're going to try to make it math centric. And as long as we're staying on topic with math or sciences or whatever, we don't go too far off tangents regarding politics, economics, down rabbit holes. We'll definitely load up all the videos to bit shoot. And if we are math centric talking about sciences and not going down rabbit holes too much anyway, we'll definitely load these up on YouTube as well. So people can have access to them there as well because the name of the game is try to have this platform available for people that want to learn mathematics. And if you have a question about math, the odds are other people have a question about math. The same question about mathematics, right? That's one thing I tell my students a lot is never be afraid to ask questions. You'll never learn if you don't ask questions, right? If you just wait for people to feed you information. That means you're going to have gaps in your education, your knowledge in your understanding the world. And if you have questions that you want to ask, then the odds are other people have the same questions. So why not instigate, you know, the flow of information just act as a note and ask the question. Let the information come to me, even if it's a simple question that you need, just a minor connection from one concept to another concept. Aside from that, that's it. Let me show you what I got. That's snacks. That's snacks here. I got a little bit of cuckoo left over. We got from like the live stream working session we did, I guess Monday, right? So Monday, Tuesday, Wednesday, Thursday, Friday, right? So that's a few days of us eating cuckoos as our main dish. And I've been snacking on these daily basis, right? Hello? Gajil effects. Gajil effects. Gajil effects. Gajil effects. Gajil effects. Gajil effects. How are you doing? So it was a great cooking live stream. We've got enough food to feed us for about four days or so. And as I do have a sweet tea, so I got myself a little bit of tahini and maple syrup here. Just in case I feel like a little bit of sweet, which I do right now, actually. Power of food. Really amazing. If you want something substantial to tie you over and just nourish you, right? And if you need a little bit of kick, this is tahini, which is basically sesame seeds ground up. And maple syrup just mixed together. That's it. It's a fantastic little nibble thing. And usually, not usually, I do eat it like this a lot, just with a spoon. But you can also eat it with just bread, just toast some bread and put a little bit of this on it or dip it. And use it as a dip for bread, really toasted bread and just eat it. It's fantastic. We learned this. Our family learned to do this from a family friend, elder gentleman. He's no longer with us. Unfortunately, he passed away many months ago. But we learned this from him back in the, I guess, early 90s, right? Because it's something that he would do and he went, oh, what's this? Our family. It was like, oh, that's cool. So we started doing it. Fantastic. And he was from Turkey. He was a Turkish. He's Armenian Turkish. And he said a lot of people in Turkey for breakfast, they would mix up the tahini with maple syrup or honey and have that. Martin, how are you doing? How's life? Hope you're doing well, brother. Hope you're doing well. It's a crazy, beautiful world with Levenet. Crazy, beautiful world. Interesting world. I've been doing a lot of mathematics with students. It's exam season, right? Final exams. So I spent time reviewing with my students that I've had for a while. And usually at this time of year, you start getting panic messages, new clients that are like, my kid is failing. Oh, my God. What's going on? We need help in the last minute, right? Basically in the last month or last two months of school. And one of the things I do is I try to lessen my load of work that I need to do with my older students because I usually try to get them prepared for the exams way before the exams are coming up, right? So I'm reviewing constantly through the year and filling gaps. So most of my students are pretty well prepared going into the exams. So I've done the front end work from that side. The back end work. So I coasted there with the new students that I get. I kick it into high gear and just power, power, teach them, right? The UK is much brighter now. The witch has fallen. Yeah, more than I heard. Oh, my God. Her little love. This is just a little politics, but it's huge. I don't know if it's humorous politics, but as Martin said, the witch has fallen. I watched May's Little. I love, I love my country. Solving thing she did, which was people were commenting that she should get an Oscar for that performance, right? Because I don't think anybody in the UK. Well, you know, you know what? I tend to believe her that she cares about the UK. She cares about, but I think she cares about money and power a lot more than the citizens of the United Kingdom, right? You can still care for something, but if you care for something even more, you're willing to sacrifice that other thing that you care for, right? So that's my take on it. Yeah, it's a little brighter. Yeah, we'll see. We'll see. We'll see. I heard the, who did I read? I read someone saying that, oh, I think it was Caitlyn Johnson just tweeted out yesterday or a couple of days ago or something like that, that she hopes that Boris Johnson becomes the new leader of her party. I always mix up the names of the parties, right? Because the illusion will be lifted of how ridiculous they are. Brexit must be abandoned. That's your take, Martin? I don't know if Brexit's going to be abandoned, man. They're going to try to abandon it, but man, if I was a UK citizen, conservatives, oh yeah, the conservatives, that's right. Boris Johnson, the leader of the conservatives, that would be like, but there's a lot of farce representatives of certain organizations and certain interests that are putting these people in power to get their agenda through, right? Why not a monkey? Why not Boris? I don't want to say monkey. Why not a joke? I don't know what you call all this. All this is crazy. I'm a liberal Democrat guy, I'm assuming that G is supposed to be a B. Yeah, B is supposed to be a G. Yeah, for me, I have tendencies from everywhere, all the different so-called categories of political, economic mindset. The one thing I stand by is learn your mathematics. Learn your mathematics. It will empower you to do whatever it is you want to do. If you want to be a May, you can be a May. Johnson, Johnson, you can be anybody, but better if you know mathematics. No Brexit would be bad. Another EU referendum not followed through. Yeah, no, I cannot see them not going through Brexit, really. I think racer kill, I think, by the way, we're going to talk about the stuff in politics, but I think, you know what, I can't even imagine what the repercussions would be. I really can't. I really can't. I think people are misjudging how important it is to many people. I think people are misjudging it. What about mathematics? What are we doing with mathematics? What should we do with mathematics? It's funny, I love the mathematics stuff I love doing. I love doing the streams, I love doing the math, the uploading the streams to YouTube, even though I, you know, ideally I would like to record it with Pal Michael stuff. I just don't have the time and the capacity and all the equipment set up to do this every time I set it up. So we're just uploading the live streams to YouTube and bitch you and stuff. But these live streams that go on YouTube, they get the lowest hits, lowest views out of all of my videos in large part, right? The interest in the mathematics of it is not as great as some of the other stuff that I put out, right? But I love putting these out and I will continue to put these out, right? Because I think it's very important. And I think in the big scheme of things, in the limit, this math content that we're creating, just Q&A and just this and that, it will go phenomenally well with the other math content we're creating that will help people in the long run to learn mathematics that they need to mask off, raven, how are you doing? Welcome, welcome. Eduardo, how's life? Welcome to another math live stream. Even though we haven't done any mathematics yet. We're just saying hi. We're just saying hi. I've been doing a lot of mathematics lately, so, you know, just with my students and new students coming in and stuff like this. So if you guys want, I could teach you something or if you have a question, we could definitely deal with it. But instigating a whole new series topic, I think I'll hold off until a certain question comes on, right? I found you through comics, Batman, Venom reading, nice, nice, nice, nice. The Batman reading was the Venom reading, Legends of the Dark Knight, and it was number six. And Martin, I consider those, I believe it was number six anyway, or number five, number six, number six. Yeah, each story at the beginning was five issues long. So the story of Venom from the Legends of the Dark Knight, and it's not the Venom that people are thinking about from Marvel Comics. We're not talking about the symbiote, Spider-Man symbiote, right? We're talking about Venom, the drug, the steroid, really, that Batman takes to become stronger. And as far as I'm concerned, that is one of the greatest Batman stories told. Okay, it was fantastic. Bane Venom. Bane Venom, yeah. Dante, how are you doing? What up, brother? What up, brother? Really, that story arc was phenomenal. That sealed the deal for me for Legends of the Dark Knight for Batman. I consider that series to be equivalent to Hellblazer because it was very mature-oriented. Hey, Chico, how's it going? Great lasagna doing well, brother. Thank you very much. Enjoying things. It's been getting warm, but today is chilly. I brought over a tuk, just in case I get cold, I put my tuk on. And this is a new tuk, by the way. This is a new tuk I got. I got it as a present. How do you guys like my new tuk? I like it. The colors match this. These things. But I think it go really well with a bright-colored shirt. A happy tuk, right? It's a happy tuk. I like tukes. That's one of the things I like. I have a small collection of tukes to grow much larger over the next few decades. Stylish. Nice. I like it. It's cute. It's cute. How do you spell tuki? I know them as beanies. Yeah, beanies. How do you spell tuk? I don't know. Tuk. T-U-K? Tuk? That's tuk. Tuk. I don't know. I don't know how you spell tuk. That's it. Yeah. T-U-Q-U-E. That's right. That's how you spell it. So what's happening with the size? Dude, I've mentioned this a long time ago, right? I mentioned this for many years now. I've been following WikiLeaks and Julien Assange. What's happening with WikiLeaks and Julien Assange is one of the most important things that is happening in the world. Okay. And it will be remembered. It will be studied for decades. And if we last centuries for centuries to come. Any news that you're listening to that you've been following that hasn't had WikiLeaks and Julien Assange as one of their number one topics that they have been talking about for the last... How are you doing? Talking about for the last few years is a garbage news source. Stop trusting them. Okay. Start to look into who has covered a lot of content, a lot of material regarding WikiLeaks and Julien Assange and who have been on the right side of history. And the right side of history is for freedom of information, free flow of information, protecting journalism, protecting publishers and the right for citizens of a country to know what is being done in their name and with their funds. Especially if they are war crimes because the citizens of that country, if they are funding war crimes and they are happy to be oblivious on what they're funding, what they are responsible for, then that society is heading towards a dark, dark place. Okay. What is happening with WikiLeaks and Julien Assange is one of the most important things that has ever happened in human history. Period. Anybody that says otherwise is delusional, is oblivious, they are completely misinformed, uninformed, or just a shill for the corporate propaganda. Okay. That's it. What can talk about this tomorrow a lot more? In Portuguese it's tucca. Nice. I like that tucca. That's in Brazil too. Portugal and Brazil. I don't know which other countries speak Portuguese. Night night. How are you doing? I hope you're enjoying your Friday. Very nice to. Thank you brother. Thank you. Yeah, I'm enjoying the Friday today. I've been doing a lot of gardening and taking care of the plants and flowers and stuff. Lord, how are you doing? Good evening everybody. In recent news in Belgium elections are coming up. European Belgium and federal elections. Yeah, the European Belgium elections too. Belgium federal elections and multiple news sources have left certain politicians out of the polls, etc. Because they have another. Wow. That's crazy. And by the way, Lord, that is what's happening in the United States as well. Tulsi Gabbard is getting serious foothold within the United States. Okay, I'm going to be non-PC. With the more intelligent people within the United States, Tulsi Gabbard is getting a serious foothold. Because she's saying things that both the left and the right, and people agree on, except for the corporate propaganda. People agree with what she's saying, right? So she's getting a serious foothold underground grassroots foothold. But the mainstream media is leaving her out. But for the most part, some of the things that I've seen come up. I don't really watch mainstream media. Julian is a great man. See, when I say that, Julian Martin, I agree with you. Julian is a great man. A lot of people misinterpret that as saying he's a kind man. He's a good man. He's someone likable. Likable, right? But that's not what it means, right? I've had people turn to me and say, do you like Julian Assange? I go, dude, I like what he represents. What he's done. He's a great man. What he has achieved. What he's put his neck on the line for. He's put his neck on the line for humanity. And these people are asking me if I like the guy. It's like, what does it matter if I like the guy or not? He's sacrificing himself for the betterment of civilization for human beings in this world, right? He's a great man, period, right? I'm starting to follow a new source right now, Brazil 247. I haven't followed any ever. They don't talk about Assange, but it's Brazil only news. So okay, that's good. If it's local news, Brazil only, right on. Pepe Escobar supports them, right on. That's good. So I think they're legit. Awesome. I like Pepe Escobar, trust Pepe Escobar. As far as I know, Portugal, Brazil. Mozambique speaks Portuguese and Angola speaks Portuguese too. Wow, that's cool. That's super cool, Zanya. I didn't know about Mozambique and Angola. I guess those were the Portuguese colonies, right? Though I'm sure there's more. Eduardo might not. I voted yesterday. You voted, Martin, yesterday. Cool. You voted in European elections yesterday, I assume, Martin. But in Belgium, people are realizing this. And when the mainstream news now comes on the streets, people actually block their cameras. So they try to disrupt. Really, that's cool. This was the leader of my mod. Thanks for taking care of business, whoever the mod was. Oh, night, night, nice. Thank you very much for taking care of business, night, night. My relatives watch MSN all the time. I have no idea who Tulsi is despite her popularity in the serious political communities. Yeah, actually, Mask of Radium, that's a great way of saying it. Serious political communities. I'm going to start using that. That's less politically crack and I think it's more accurate. Tulsi is awesome. Listen to her interview in the Joe Roland podcast. Very interesting. Yeah, loved Fifth Estate, but made him out to be a little eccentric. Fifth Estate, that's the TV show, but are we talking about Assange? Is that what they did, Martin? EU elections, yeah, coming up on Sunday for Austria. It's Sunday for Austria. Wow. Different countries vote on different days. This weekend, really, that's crazy. Yeah, all elections, EU related are on Sunday. I'll have to wake up early, I guess. Ha, ha, cool. Sunday in France as well. Wow. Okay, so this Sunday should be interesting. European elections. Now I'm getting all excited, gang. Yes, European elections. I hear the Brexit party are going to win a lot. Yeah, Brexit party in the UK guaranteed. As far as the polls I've seen, it's like 40%. They're polling 40%. And by Sunday, I think they're going to be polling a lot higher, right? Unless people actually, the conservatives or whoever, the May party, as they go, oh, May's stepping down. Maybe they'll do better this time. If they fall for this thing, I think that's the reason May came out and said, I'm resigning in June, right? To at least prevent some of the people that are moving towards the farrages party and the other party to sort of go, oh, okay, come back, come back. May's stepping down. I hope it doesn't work. I hope those people just, the leading, the governing party in the UK, I hope they basically get knocked out, right? They do not deserve a single vote in the UK. Really, really, they've proven themselves to be complete sellouts and not having the best interest of the citizens of the UK in mind, period. Moving about, yeah, moving about, oh, the fifth state, moving about Julian signs, that's right, that's right. Yeah, yeah, yeah. We have a TV show, a news show, or we used to anyway, it was called the fifth state in Canada. I got confused with that. I think the fifth state still goes on. I'm not absolutely sure. I don't watch it. I haven't watched it for a very long time, 15 years or so. To all my European friends, won't, wise and smart, our freedom may depend on it. 100% Lord. And one thing I love really about these streams and stuff like this, we have a lot of Europeans, or a lot of Europeans are here. Okay, in general, we have a lot of Europeans. I don't know why. I don't know why I've attracted so many Europeans. But thank you for being here. You guys have been educating me about Europe, and I love this interaction with the different communities, different countries in Europe. And it's phenomenal. As a Canadian, thank you. I appreciate it. Chicho, do you have a video or anything on Brexit? Let me find it for you. Watch this. You're going to love this. You're going to love this. I'm going to find it for you. Hopefully, we don't lose the stream. I don't think we will. Hopefully not. Chicho, I'm going to link you. My Brexit video. I'm laughing. I'm giggling. Here, let me give you this link. And I'll read you what the title is. Here, I'll give you the link. Oops, where is the chat? I'm going to bring out the chat. Here's the chat. Here's the link. And the title of the video is Comic Book Hall No. 6, Legends of the Geomancer, Valiant Comics. And the description is ASMR Math, soft spoken review. And my video on Brexit is as soon as... As soon as the vote was done on Brexit, where all of a sudden the corporate... Propagandist, the corporate political class, when they realized, oh my God, the people in the UK voted for Brexit, they wanted to leave the European Union, the pound dropped a little bit, right? So the pound relative to Canadian dollars, U.S. dollars has stopped, dropped, right? And there was one auction I was following that had five copies of Legends of the Geomancer No. 1 up for sale, right? And I sent the guy a message saying, well, you know, I made him an offer for all five of the comics, right? And he accepted my offer, so I bought Legends of the Geomancer. I just did it as a Brexit celebration because I was ecstatic. I was very happy, right? And Canadian dollar, pound had dropped relative to Canadian dollars. So I was getting a little bit of discount, like saving like $8 or $10 or something. So my Brexit video is me buying Legends of the Geomancer No. 1. I'm sorry I'm cracking up, but this is exactly the way I felt when Brexit passed. And I did the buy, right? Hey, Chico, hope you're well, brother. I'm doing well, Richard. How are you doing? We're calling the milkshake... oh my God, I can't believe that milkshake stuff going on. Seriously, is it being called a milkshake election? That's crazy. Liam, how are you doing? How's life? Welcome to a stream. Belgium here, of course. Dutch-speaking part. Flanders. The milkshakes are kind of funny. They're kind of scary. Mask of Raven. I do not agree with violence. I don't agree with silencing people, right? So these milkshake attacks, and they are attacks, right? They're meant to silence people. And for me, I will... You know, I'm saying it now, but will I fight to the death for you to have the right to say what you need to say? I don't know if I have the willpower to fight to the death, but I'll fight to my capacity to help you to make sure you have the platforms available to you to speak your mind, even if you totally 100% disagree with me or I disagree with you, right? Even if you're 100% opposed to everything that I stand for, you have the right to speak your mind. I will never, never try to silence you. I may engage you, disagree with you, fight you verbally to the ends of time, but I will never, ever try to violently suppress your right to speak. It's a great time to watch in Europe. It is 9 p.m. in Germany. Nice, nice. Pepe, how are you doing? How's life? Welcome to a stream. You're welcome, Chichou. Thanks for your great content. My pleasure. Merci. I'm assuming you're from France. Anna, how's life, Chichou? I'm wondering what the stream schedule is for this weekend. One stream tomorrow morning, 8 a.m. tomorrow morning, about current events, which we're talking about right now. So, 8 a.m. tomorrow morning, stream about current events. I know it's going to be really early for people in Canada and the United States, but I had a request from someone in Europe last stream saying that it'd be great to have a stream early on regarding current events, and specifically one of the ones was about the polar, how everything's being divided into two parts. I forget which term is for, right? So, that's what we're doing tomorrow. Discord. Thanks, Lord. I'm laughing so hard. I'll watch it now. Night, night, night. Mask, yes. And everyone is getting strawberry flavored. But no chocolate. What? Chocolate is delicious. Strawberry is the balsamic shake flavor. No chocolate. Oh, you're not a chocolate lover. I love chocolate. Strawberry is good too. Chocolate milkshakes are so good. Vanilla I like too. May I ask where you're from? I'm in Canada. I'm in Canada. I'm from accessory, blood-wise, Armenian, born in Iran. And I'm basically West Coast Canadian. That's my mentality. I've lived here most of my life. So, I fit in really well here. Milkshake's so yummy. But shouldn't be in elections. They shouldn't be in elections. You know what they should do? If I was forage in the right leaning party, parties, and I guess it's the right people that are going to milkshakes thrown at them, I would throw a milkshake party, really. If I was having an event, I would hire milkshake trucks, right? And give out free milkshakes to everyone. I would use the weapons that are being used against me to commit violence against them. I would embrace it, okay? I would grab, bring milkshake trucks and give everybody a milkshake, okay? On the house. That's if I had the funds, of course, okay? It's like appropriating the pink triangle, right? It's like this tactic has been used throughout history for good and ill. This would be good as far as I'm concerned. I'm actually posted a news article in Discord about protest during elections. Okay, thanks, Lord. Awesome. Are milkshakes violence? Throwing milkshakes at someone, it is, for sure. Throwing milkshakes at people, it is. I think once the first milkshake incident happened, it just became a bit of a viral trend, if I'm honest. Yeah, and usually the weak-minded follow the viral trend, especially if they're about committing violence. Nature show, another week is ending. Thanks for putting current events on morning this time. Germany, you're the one that asked for it, wasn't it? I think so, and my pleasure. And by the way, that's what I try to do. If you guys have topics you want to discuss or if you want this thing sort of what we're doing to go in a certain direction, post a comment. Ask me either on Discord, YouTube, here, wherever. I'll try to fit things in. I try. I can't promise I try. Well, if you're magical, if you're lactose intolerant, the earth is flat. We talked about flat earth. That really depends on your perspective, Neil, right? It should show that. We can talk about it if you want. Again, I'll prove it to you that the earth could be flat if you have a very narrow, if you have short vision, right? But the earth is round if you have a bigger vision. The volume of a cone, can we go over that? Sure. How to calculate? Sure. Life is good. How about you? I'm doing good. Thoughts on that? Oh boy, God. There is one... Basically it's a trade war, Pepe, right? So it's about trade war and technology and stuff. It's huge. Very, very important. Very important. The shoe isn't thrown in the occasional milkshake, but people engaging each other to keep doing it. Yeah, it's somewhat problematic. Like, why not bring paint guns instead of, for example, yeah, first they came for the guns, then they came for the knives. Soon Derry will be regretful. Yeah, seriously, how are we going to ban Derry? Will you cover linear algebra at some point? If you like, but basically linear algebra. I'm not going to do determinants and matrices right now. Okay. Volume of a cone. We need the formula. Volume, I think it's 4 thirds, 1 third, pi r squared times h, or 4 thirds. I've got to look that up. Does someone want to look up the volume of a cone? Volume of a cone. I'll look it up as well. So it is. It is this one. 1 third. Okay, cool. Okay, that's correct. Pi r squared, I think divided by 3. You must have had Dante. Yeah, okay, cool, cool, cool, cool. Let me just get caught up on the things really quick. Unfortunately, I might be outside visiting a friend tomorrow when you're current. Oh, that's too bad. That's unfortunate Germany. So if I miss it, I might rewatch it later. Okay, awesome. Just wouldn't display properly. Yeah, you had the division sign. Okay, awesome, Dante. That the marijuana came into existence as a group on the tomb of King Solomon through his knowledge worth of. I googled that one, nice. That's funny, Adam. You basically need integration to calculate volume of a cone. Well, if you get the formula from integrating the surface area, I guess, or something like this, but once you have the formula, you don't need calculus, right? You just need the formula. So this is all we need to calculate the volume of a cone, unless we're talking about driving the volume of a cone and you need calculus to do it. But basically, volume of a cone is, it's all based on the radius and the height, right? And the height. So all you do is just plug in these two numbers. Now, there's different ways that can ask you the same question, right? So for example, in the most simple form, we'll do one here. We'll leave this drawing down. So let's assume question was this, right? Question was five volume of a cone that is, I don't know, 10 centimeters long, long, and has a, I don't know, what do you refer to that? The radius of the surface, the radius of the top of the cone is five centimeters, right? With radius of five centimeters for the top of the cone, right? Sorry about my writing, but usually I don't even write it. Because all we care about is this, right? All you care about is this. 10 centimeters long, right? And radius of five, right? Once you've got 10 centimeters long height and a radius of five, you just plug in, right? So this becomes one third pi times, the radius is five times, oh, five squared, my apologies, times 10, right? Five squared is 25. 25 times 10 is 250. 250 pi, 250 pi over three, right? That's the volume of the cone. And since we're talking about centimeters, don't forget the units, put the centimeters in there, right? Now this question can come to you in different ways as well. Sometimes they give you this, right? Sometimes they give you this distance here. They call this S usually. Now before we do that, let me just check the chat, make sure I didn't do anything wrong, and see if there's any buildup on this we need, right? I'm doing math and math A level and I have exams in a month. I haven't started revising, what do I do? Start revising, start reviewing. Is it enough time? Yeah, for sure, for sure. I don't know what math A level is, but a month of, if you're serious about it, a month you should be able to learn almost any subject in mathematics as long as you got some of the background that you need to learn, right? You just have to take it seriously. It may mean that you need to study multiple hours a day, right? Just to give you an example, for me, there was one course I took that was the hardest math course I've ever taken. It was the systems of, systems of, it required you to look at systems of equations and do multiple integrations and it was applied mathematics second level, the second, second course, the second semester. It was so difficult. I studied 10 days straight for that course, studying anywhere between 10 to 14 hours a day. And they didn't have linear and algebra, so I had to teach myself linear algebra. I grabbed the linear algebra book, learned the linear algebra, and then learned the stuff and I passed the course. I didn't do phenomenal what I passed. You can do it, really. If I can do it, you can do it. Are you good at math? Yes. Maske of Reagan is asking Liam, which field of math? Which field of math? Exactly. Right. Before we start, let's get this clear. Do you have a, do you have a French James? Well, I don't know what that refers to. You can integrate the cross, section, sections, dependent on the height. All one cone-like shapes have a volume of this. Okay, cool. So what's going on with race killers mentioning and guarding needing calculus to do this? Because what you can do is, basically you can draw the cross-section of the cone. So here's your cross-section. Let's just make it like this. So our calculation has become simple. So it's centered on a y-axis, and through calculus, the way you figure out the volume of this is basically you take this thing and you integrate it, which means you're looking at the third dimension, and all you're doing is rotating this. Right? Once you rotate it, you create a cone which you can get the volume for. That's where the calculus is really coming in. I hope I'm right. I'm going by memory from like 20, 30, five years ago. Right? Liam, you indicate what is zero divided by zero? Undefined. You can't divide by zero. I have heard a lot of different theories on it. Different opinions on it. Strictly speaking, if someone says zero divided by zero, this is undefined. I don't know if that's the right symbol to use for it. Let's say undefined. Undefined. However, if someone gives you a function, right? If the above, if this is a function where you have something here and something here, and if you want to understand what this function does for a limit, right? As you approach a certain number if you go to infinity, and when you're simplifying this, you get zero over zero. You need further analysis because you can narrow, you can approximate what it might be based on the functions you're dealing with. So it's not as straight out as having the number zero over the number zero. Everyone can be good at math if they try to learn. I agree. I am from the UK. How many hours do you recommend? As many as you need. If I was you, Liam, I would start off figuring out where the gap is, what you're missing, right? Because the odds are the reason you're overwhelmed is because you haven't done the earlier stuff. So back to the beginning and start reviewing. If you understand the material, then just keep on moving forward. Do maybe one or two questions. If you're doing sample questions, I don't know math A, what it entails, what it's covering, but whatever it is, because it's A, I'm assuming it's earlier on, so you got to do questions, problem. So try one or two. If you're getting them right, just keep on going. Spend more time on it until you understand it and then move forward, right? Don't... If you don't understand a certain concept, don't jump too far ahead. Sometimes you can do that depending on the course because this one section might not be related to the other core material, but that's something you're going to have to decide. Me too. I did A-level math in 1990. Wow, cool. Very, very true. I only asked because he's only got a month for A-level math. Hopefully he has a strong background. That's the word I should have used. Did you do math or university math? Liam, are you... oh, Mark. Okay, I was asking Mark. 6-4, 6-4, 6-4. It's either plus or minus infinity. It's either plus or minus infinity. So basically what that means is... Here, let me take this down. Basically what that means is... Here's your X-axis. Here's your X-axis. In general, this is your F of X. In general, when they say plus or minus infinity, they're looking at what happens to the function as you go this way towards positive infinity or that way towards negative infinity. So they want to know whatever the function might be. I'm drawing just a polynomial. Whatever it is. I did go to university, but I studied psychology. Graph theory is a really great topic. Graph theory is a really great topic. The limit of X over X, as X approaches 0, is 1. So, okay. You can take the derivatives. Mask of Raven and stuff, right? It's advanced level. Chichoprotip. If a text book doesn't have a detailed section on solutions and tables of contents, put that book down and go find another book. That's what I mentioned during that book readings and stuff, right? How to study. And Hannah, thank you for reminding us of that, right? So if you've got a text book and it has problems and there's no solutions or examples of how to do some of those problems, put the book down. Go find another book. Thank you, Hannah. That part of the video I've re-lined it so many times because it triggers my smart life. Nice. I love that video because it's informative. It would be possible if you could explain normal distribution for me, Chichoprotip. Yeah, surely, I must do normal distribution. I want to take all this down. I can do basic normal distribution with you, okay? Let me give my... I laugh too much to have made myself turn the blank zipline just cracked up. There's 24-7 Bob Ross channel there. It should be a Chichoprotip for its workshop purposes. Sorry. No, Liam, you're not bothering. This is about mathematics. You got questions? We deal with it, right? So a normal distribution. Okay. First thing you should ask yourself when you're thinking about normal distribution is what branch of mathematics is this, right? And this is statistics, really, right? So what is a normal distribution used for? And what is the mechanism behind analyzing using the normal distribution, right? So whenever you're talking about mathematics, you should always have a purpose in mind. Why are you studying this? What's the purpose of this technique? What is it that they're talking about? Really, keep this in mind. This is ridiculously important, right? Because that puts you in context. It allows you to associate that with the real world, right? So it gives you purpose for learning this thing, right? Because it is a tool that you might end up using in the real world. Normal distribution is stats. Also, lots of functions and calculator for that. Yeah. So basically, it's this. Okay. Just imagine if you want to try to understand a certain system. Okay. So that's just so we have a box here. And this box could be anything, right? It could be a country. It could be you collecting data from nature. It could be you trying to understand a certain business model. It could be anything. Okay. Really appreciate this. This data set, this system that you're trying to understand can be anything. Okay. So let's assume you acquire the data from this, right? So this is you. This is you. I used to be able to draw better eyes. How do you draw eyes? I used to do this with physics, right? So this is you looking at the system, right? Looking at the system, you're going, wow, trying to understand the system. What's going on? Right? How do I make use of the system? Right here. Let me draw. Let me make this better. So I don't look ridiculous. Let me draw the line. Right? So here's you. Here's your mouth. Here's your eye, right? I don't know if that's any better, but it shows a face, right? So let's say you're looking at the system. Actually, I guess your eyes are looking at the system, right? Your chin is not looking at the system. So let's make this more accurate. Right? So you're looking at the system. Okay. You're going, I want to look at the system. Okay. And what you're doing is collecting data. When you're looking at the system, you're going to look you're going to collect data. You got there's absolutely no way when you look at a system that you will not be able to collect data because data is information. So even if you're just sitting there, right? And looking at people walking by, you're going to go, oh, wow, today, a lot of people are wearing red shirts. Your mind automatically does that because one thing you have to appreciate is us human beings. We're basically pattern recognition machines. Really. We're so good at pattern recognition that we find patterns where there are no patterns, right? Hence people go down rabbit holes and then later on they realize, oh man, this thing and this thing are nothing in common. I just saw pattern where there was no pattern, right? So you're sitting looking at the system, whatever this might be, might be the elections in the United States, might be nature, you're looking at the birds in the area, it might be you looking at your business trying to collect, trying to understand this business model, right? So you're collecting information. So data is coming here. Data, right? You might be really interested in the system where you just don't want to just have a minor understanding of what the system is doing. You're actually writing down recording data, right? Sometimes when you're driving, you see people sitting there recording data, right? They're working for the city trying to understand an intersection, right? And most likely trying to change the light patterns or introduce lights or whatever it is trying to direct that traffic in a certain way, right? So it's not just enough just to set their goal. There's lots of traffic here. You need to collect data. What type of traffic? Bikes, motor bikes, cars, trucks, how fast are they going? How many pedestrians there are, right? So you're collecting a lot of data, right? So this person sitting here, right? Here's their hand, right? Here's a pen and they're collecting data. So you're looking at the system, collecting data you know, writing this data down. What do you do with data? Once you do this, you take this data and you graph it. Whatever the system is, right? Different systems that you're looking at collect different bits of information, right? And one thing you end up doing in general is you take two of the data points, two of the variables in the system, right? For example, if you're looking at an intersection it might be the time of day and the number of automobiles, right? So we're not even separating, you know, motorbikes, cars and trucks. You're going to categorize them all as one thing and you're going to say okay, those are moving vehicles. Whatever you're going to call them, right? And the time of day would be your other variable, okay? I thought there was an emphasis on visuals when I was learning no distribution but my prof got nothing on this diagram. There it is, right? So this is what we've got, right? So we're looking at a system collecting data, recording that data, and then you pick two of the variables here. We don't know what they are. We don't know what the system is, so let's call them x and y, right? So we're going to take x and y and we're, first of all, which we want to know if these are related, right? Are these two variables related, right? So what we do is we take this data and we put it on x, y, graph x, y, okay? So we start graphing this data, right? If we get a graph like this you could pretty much say that x and y are not related. They have nothing to do with each other, right? Easy enough. So you come to a conclusion that x and y are not related. Maybe you say, oh, okay I collected more data than just x and y. I'm going to substitute this with w another data point that we collected to see if x and w are related, right? And when you graph x and w you get something like this. You go, oh those two might be related. That looks like a line. So you go, oh you analyze the data, you do regression analysis and stuff like this and you come up with the best fit line and you go, okay x and w are related like this. Easy enough, right? But you've collected more variables than just x, y and w. Maybe you've collected other variables, right? So another variable you might have is, I don't know what's the variable we use in statistics? I don't know. But I'm going to do this. I'm going to call it f of x, right? f of x would be just a function, right? That is dependent on x. So it's just another variable. So instead of writing y, right? I'm going to say, I want to know if y is related to x. So instead of writing y I'm going to call it f of x. We found out that y was not related to f of x but w was. So w was a function of x. So we're going to look at another variable with the same thing. So we're just calling it f of x. So let's say you graph this and you end up finding this out, right? How was that professor that drew? Oh, he did it with chalk. Let's say you find this out. You go, oh, that's a neat graph. What is that? Okay, so you say, okay, that's graph. Make this top solid, right? So you go, okay. I'm going to draw the outline for this and it looks like this. That's cool. Okay. That's called a normal distribution. That's what we've ended up calling it, right? Just like when you call this a line, that's a line. Where did we come up with the name line? I don't know. It's a line, right? Who came up with it? I don't know. Okay. That's why this is called a linear linear function, right? That's called a line. This is called a normal distribution. Okay. And this graph has certain properties, just like the equation of a line, right? If I draw a line, the general equation for a line is y is equal to mx plus b, right? This is the y intercept and that's the slope of a line, right? So when you draw a line, you can come up with a function that represents that line, right? And then you can read things off from that line. Normal distribution is the same way, right? This has certain properties, okay? One of the properties is this. If you cut this thing right down the middle, right? Right down the middle. For normal distribution, the graph is a probability density function. Sorry, it's a probability density function, but what do you call it? I'm just doing it this way, just to associate it with it, okay? By the way, Racicler, thank you for the correction, right? There's a reason why I've said I'm not doing any hard core stats or any hard core calculus because I don't have my terminology, right? Okay. So one of the properties is this. Right here, you call this x with a bar on top, which is the average of the data. You find out if you take the average of data, the y is supposed to be a probability that x occurs. Okay, cool. That's supposed to be the probability of x occurring, right? Probability Probability of x. Okay. So, what's the symbol for this basically? That's the y, okay? So if you take the average of all the data, right? If you take all the averages and you plot that point on there, 50% of the data will be here, 50% will be there. So it cuts the data set, the probability of x occurring right down the middle. That's cool. Okay. The other thing that happens is this is completely symmetrical. So if you go here, let me, one unit away and we call this one standard deviation away from the need. If you go here, this part, I forget what it is, is 65% or 68% of the data is within that range. Okay. And if you go two standard deviations away, from here to here, like 95% of the data is within there. Have you ever grown any... Are they profitable? No, profit? I don't do profit in regards to that. Or that's not entirely correct is probability density around x. In fact, the probability is calculated by taking the area under the curve. Yeah. Oh yeah. And this is area, by the way. That's why I'm shaming this set. Right? So it's not really... I guess the data... Well, it is the data points. Okay. The integral of that is always one. Yes. The probability, if you take the area as it comes out to one, this goes on forever, by the way, comes out to one which really represents 100% of the data. Okay. That is always one. And if you want to calculate the probability of your x being between two numbers, you have to calculate the integral. Yeah. And there's tables for this, right? So basically, let's assume this x is here and you go to here x minus... Oh, what's the symbol you use for it? Is it sigma? Is that it? I haven't looked at the stuff for a while, right? And let's call it... Oh, it's just x. Sorry. The sigma is in the bottom. x minus x. And if you take this point here and you make this x plus x, right? x1 and x2. That's like saying between this number and this number. If you want to find out what percent of your data lies within those two ranges, right? There's tables you can look at that give you that data. And they're all decimal. So for example, if this was, like someone said 1 and this was equal to 2, okay? And if this was in the middle, then this would be one and a half. This data point would be 1.5, the mean, right? Or the average. And if you want to look at this, then you can look at tables and find out what the probability is within those ranges that they give you. Okay? I'm sorry if I'm not using the right terminology and what not. But basically this is the gist of the normal distribution. And why is this important? Because when you learn how to use the normal distribution, the property is associated with the normal distribution, then you can take any data set that fits this model, right? And first of all, understand that system and make predictions based on that system, right? So if you can take a data set and it fits the normal distribution, there's a tremendous amount of information we know we understand of data sets that fit the normal distribution. So just through mathematics, without even really knowing what the system is, you can interpret the system by the numbers and then you can associate those numbers to something within that system to say, oh, wow, this happens. Oh, wow, this happens. Oh, wow, this happens, right? So it gives us a tremendous amount of info on a subject matter, on a system that we're trying to understand. As for the different types of questions, man, there's a gazillion different ways that stuff comes at you for this. There's something called the Z number, which is the standard deviation. There's the variance of it that the normal distribution could be like this, but it could be sharper, right? So that would still be a normal distribution, but it's tighter, okay? 60% of values are within one standard deviation, cool. So 60, oh, sorry, 65%, 68%. So in here, thanks for finding that, by the way. So in here, 68% of your data is between one standard deviation away, and I forget what the symbol for standard deviation is. Is it the sigma? Is it whatever it says? Thank you so much. I hope my donation went through. I don't know. I didn't see it so I was doing the stuff. Thank you, Liam. Thank you for the donation. Okay, I use this at work looking out shift patterns. Oh, dude, that's cool. Really, use normal distribution for shift patterns. That's crazy cool. Normal distribution has a property that sums of random variables tend to have, which can be made exact normal distribution. That's what makes it important. Let me just read that again. Let's check it out. Normal distribution has a property that sums of random variables tend to have, which can be made exact normal distribution. Rather, sums of random variables have approximately normal distribution. Oh, sums of random variables. So any no, it can't be. Any random system you look at has a normal distribution. That's not true. Race killer, is it? Racer killer. How do you calculate probability if you have a set of 39 and have and you have to get 7, right? Well, if you have a set of 39 and you have to get 7, right? I don't know. I don't know what that means. Set of 39, what? 7, right? Like numbers? I don't know. There's different formulas. I don't know the formulas on top of my head. I'm sorry. I do get some of my students that go to university and need stats help. Whatever program they're in, you always usually do statistics, right? So they come to me every now and then, every few years, they go, I need stats help. So we sit there and I usually always have to look up the formulas, read the the definition of the variables and they go, oh yeah, this is this and all of a sudden memory kicks in and we start doing the Z table and start calculating the probability of certain things. For example, the sum of 100 dice throws, that's the sum of 100 random variables. Yeah, okay, cool. Yeah, yeah, that fits through a normal distribution. That's right. That's right. I thought if you're looking at a complete system, I don't know if that's Yeah, and you know what? In nature, I know there are I don't know which system, but I know of you know, there are a lot of systems in nature that fit a normal distribution and supposedly they're like random is not the best. Oh, no worries. No worries. How do you calculate it? You need more data. You can't just say 39 and you have to get 7. So that would be like saying we would need to know we don't need to know variance. We need to look at the data set. We need to calculate the mean. So you need to have the mean. You need to have the standard deviation, right? Like for example if this is, let's say this is 8 and this is 7 and this is 9, right? So let's say you're collecting the, actually let's do numbers I guess. Jesus, what are we doing? Let's say this is 7, this is 6 and this is 8, right? If you're throwing dice or whatever it is. I don't know if the 68% of the time, we could figure it out. Here to get a 7, it's 6 out of 36 and to get a 6 or an 8 is 5 out of 36, right? So plus 5 out of 36 and plus 5 out of 36. So this becomes 16 out of 36, okay? So 16 out of 36 is not 68% of the time. You're not going to get 7, 8, or 6, 7 or 8, right? So let's add 4, sorry, 5 and 9 here as well, right? If you add 5 and 9, sorry if I'm going off a little bit, hopefully, if you guys want to know what I'm doing here, we put out a video with dice, the probability distribution for 2, 6 sided die, okay? And if you do chicho dice, you'll get that video. So that's sort of the distribution I'm going for with the probabilities. So getting a 5 or a 9, it's 4 out of 36 plus 4 out of 36. So that's 8 more. 8 plus 16 is 24, okay? 24. Is that 68% of the data? Let's do 24 divided by 36. 24 divided by 36. It's 66% of the data. 67% of the data. That's pretty close, right? So if you want to find out if you have a distribution like this, between 5 and 9, 68% of the time, you're going to get 5, 6, 7, 8 or 9, right? However, the distribution might be different for something that's tighter. So for your example, if you're talking about 39, right? 7 might be I don't know how it would be layout, might be here where you know, it's within the 68%, or it might be here which is outside the 68%. So you need to know the standard deviation for this stuff like this. You need the data set to be able to do it. The problem. Sorry. Continuous. Oh, for dice. Yeah, it fits good enough for our purposes, right? Not sure about that case actually. This is not continuous but either way, sums of random variables are usually well approximated by normal distribution. That's cool. I didn't know that. What does it mean to standardize the X value? What does it mean to standardize the X value? I'm not sure, Liam. Standardize the X value. Anybody know what that means? Hopefully someone's already replied. Nothing is random. Everything is deterministic. You mean if you throw one die it will be evenly split between one to six? No. If we threw two die a mask of randomness. We're talking about the probability of getting 2 to 12. Here, let me erase this. So the distribution for, actually it's not really a normal distribution but you could approximate it by I guess. I don't know if that's kosher or not. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Here's two dice. Here's the number of ways you can get each one. 6, 3, 2, 1, 4, 5. 7 is the most likely way which has got 6 different ways. 6 has 5 different ways. 8 has 5 different ways. 5 has 4 different ways. 4 has 3 different ways. 2 has 2 different ways and 3 has 2 different ways and 2 there's only one way and this mirrors over here, right? So is this a normal distribution? Not really because it goes down like this and it's discreet. You can only get 2, 3, you can't get 4.5 stuff so it's not really but it's a good way of talking about the data. Multiple properties to take into consideration. No, it's 2, 3, 2, 3. That's the idea. It should approximate a normal distribution the more throws you do. And this is based on infinite. Probably distribution. How many times we'll get the 7, the 6, the 5, the whatever it is. Earthquake, monkus. Yes. And the probability of 3 to 18, 4 to 24 and so on will look more and more normally distributed a higher number of throws, right? Yeah. This distribution. If you do an infinite number of throws then this is what you end up getting basically, right? For infinite number of throws this is the distribution you get with dice, right? And that's the way casinos operate. Casinos operate on infinite number of throws right? And all they're doing is really is milking, taking a little bit off the top, right? For different bets they take a bigger chunk off the top so for 2 and 12 the payout is a lot more but they take a bigger chunk so it's a fool's bet here, here is more realistic because the probability is that but I still play these sometimes because feeling, right? Which any probability matters as they don't go with it, right? But basically they take a little bit off the top. Casinos. This is casino profit here. Casino profit, right? And it's trillions of dollars, okay? Because gambling is not just about rolling dice, it's everything, right? And what happens is in the limit casinos get everything because this is based on, this is the distribution for one dice, right? Based on what the probability is for infinite number of throws but if you constantly do this and if they're constantly taking a chunk off, in the limit you have nothing to get everything, right? So it's like exponential decay. Exponential decay, it's an exponential function, right? So basically you get this. If you have a function where what you put in your principal is equal to let's say they're only taking off 2% every time so they're giving you back 98% of your funds, right? 0.98 to the power of X. In the limit in the limit you have nothing. The first time you do it you should only get back 98. If you put $100 in you get $98. In the limit f of X equals 0, okay? If in a binomial distribution NP, oh yeah, the binomial distribution NP and times P minus 1 is greater than 4. It gets close to a normal distribution. Is that true? Okay, so this thing, what can I erase? Let me read a couple more just in case I've related to this and I'm going to erase something. Could you explain how to solve secondary equations? Secondary equations, I don't know what you mean secondary equations. We're talking about quadribes, we're taking second derivatives. Strangely that dice probably looks like my busy period at work. Is it? That's cool, man. So yeah, you could use a normal distribution on this. Well, when people come and might essentially be around a variable which would be interesting. Sorry. Standardizing the X values is in the sigma is in the formula booklet. Oh yeah, that's what it is. Here, check this out. Okay, I'm going to erase this. So the formula is this. Liam says Z is equal to X minus the standard deviation. Sorry, the mean of the distribution, so X this guy, so that would be the mean. Okay, divided by standard deviation which I believe that's the symbol. Okay, so basically means when you're doing your stats, okay, Liam, when you're doing your stats there's going to be a Z table that you have in your exam or in the back of the book. Right? And the Z table is like this. And there's all these guys. Right? And what are the things on it? This is the Z number. So it would go, I don't want to put the wrong numbers on there. So I'm not going to put any numbers on there, right? So basically what you're doing, you look at the Z distribution. So for example, if this was 2, if you get a Z number of 2.6, right? You would go to 2 and then the 0.00.10. This would be 0.6 and you look at this number here. Right? And that would be and depending on the Z number, sometimes they give you both values on both sides. Sometimes they're giving you the value for one side of the thing. That's why it varies depending on what books you're using or what not. They give you the the number here as a decimal, right? So for example, 68, if this is both of those contain 68% of data, divide this by 2, you're going to get 34% of the data is in here and the number here that you would see would be 0.34. Right? I think that's what it is. I haven't looked at it as a table for many years now, right? But that would be 34% of the data, right? They say 30% of the time something occurs the mean is this and standard deviation is this, find X you could plug 34% oh no, that would be the Z number you plug Z number there you go to the table, find your 34% find what the Z number is put your Z number there and then put your mean there standard deviation you could find where you are what the X is and stuff like that. So when you're asking a question of what's the probability of getting 7 out of 39 or whatever it was right? That's sort of what you end up doing the big scheme of things the flow of the process of using the normal distribution Is there any way to find a volume of a comb without using volumes of volumes of integration I know how to prove it that way but if there were a way without calculus I think what you mean is a way without the algebra of calculus just the numbers, just the variables calculus is just a rate of change so no matter what, there's calculus in there but the way what do you call it the standard way people do it for what I understand and I've read a couple of pages from this book there's somebody that put out a book that teaches calculus strictly with shapes and I don't know what's in the book what it entails at some point I'd like to read that book but there is a book out there at least one book out there, I'm pretty sure there's more there's at least one book out there that I know of I have it bookmarked I can access it right now but there's a book that teaches how to find areas and volumes or volumes and just do calculus through shapes I don't know how they do it yeah I basically yes the z-table is basically a calculation of these integrals could you explain weighted arithmetic oh we're doing the statistics oh my god weighted arithmetic mean I can give you the general idea on it okay I'm going to take all this down any final question on this just anything that I want to point out thank you I'm you here so would you be able to tell me the schedule of your streams you make math very understandable so I would like to ask you more of my revision questions in the future right now I don't have a set time day or time well I do have a sort of day but for the next four weeks most likely we're going to do at least one math stream either on a Friday or Saturday okay I'm going to try to keep that schedule and so last week we did it on Saturday we did the math on Saturday this week we're doing it on Friday next week I'm not sure if we're going to do it on Friday or Saturday so there's two streams I'm doing for sure every week one is math one is current events and I'm switching it between Friday and Saturday that's the best I can do to narrow things down right now just because I'm really busy with students trying to do a fair bit of things going on and you know I have other people that need a little bit of attention in my life so that's the best I could narrow it down right now but if you check I do post that information I do announce the streams two to three days before they come up and if you scroll down on my twitch page there's a little countdown that tells you where the next stream is and if you hit the events on the top menu thing it takes you to what the events I've had scheduled thank you so much my pleasure I'm glad it helped I'm more specific and I wasn't using the right terminology but it's the general gist of it it's basically proved to be impossible in fact to prove this is very hard it's essentially Herbert's third problem wow which one is this let me read this he's replying to mask of Raven is there any way to find the volume of a cone really so the volume of a cone is basically impossible without the calculus really Liam you have the north of England you from the north of England that is to prove it is impossible to compute the volume without calculus is very hard really racer kill I didn't know that so the book that they're using shapes from they must be well it is calculus I just I need to read that book I need to read that book I think what I'm gonna do is I can relearn calculus with that book if I can track it maybe maybe weighted arithmetic mean oh yeah the binomial distribution let me just mention something about the binomial distribution because it came out weighted so there was someone comment about the binomial distribution the binomial distribution is basically this when you only have two choices right black or white if you want to think about heads or tails there's only two choices flipping a coin is a really good example rolling a dice and saying even a rod that's a really good example so there's systems out there which only have two choices or you can narrow things down categorize things so there's only two choices right when it comes to that they say two choices you would say n and the other one the probability of n and the other one you would say the probability of n minus 1 so if you're flipping a coin the probability of getting ahead so probability of ahead is 1 out of 2 and the probability of not ahead would be a tail would be a half as well okay you can categorize things differently as well you could say when you're rolling a dice 1, 2, 3, 4 you could group as the first outcome and 5 and 6 would be the second outcome so the probability of 1 this group would be 4 out of 6 4 out of 6 and the probability would be 2 out of 6 okay now one thing you can do just don't do it so one other thing you can do is this let's assume you just say probability of getting something is 68% right? what's the probability of not getting that thing that could be your other choice so the probability of I would be 0.68 right? and the probability of not I would be 1 I wrote this wrong I think it's 1-n 1-n I don't know if I'm using the terminology correctly right? it would be 1-0.68 okay? we should just do that that's 32 0.2 so the probability of not getting I would be 0.32 I just want to add to that a little bit that is to prove it is impossible to compute the volume without calculus you can't compute the area or circle or rather disc without calculus either cool just don't be a arsenal fan oh wow it's not even possible to prove the other similar methods do to the Hilbert's third problem not a little cone awesome thank you I didn't know that either I might have known it I totally forgot it wait at arithmetic mean wait at arithmetic average oh man I should look this up before I do it for those of you that know already I gotta look this up to make sure I'm let me tell you what I think what I have in mind and I'm going to check it before we go on anymore it's basically saying that it's not enough to take the average of something you have to put another factor in there you have to weight the variable one of the examples that I have probability everything is not the same I'm trying to come up with a real life example and I can't think of one right now my apologies but let's assume you had six possible outcomes right one two three four five six okay it's just like die so it's really important to have a fair die fair die basically means the probability of each one of these coming up is the same right the probability of two probability of three, probability of four probability of five, probability of six is all the same probability of one would be one out of six one out of six one out of six and one out of six right and a dice that is not fair could be balanced where the probability of one could be this would be a fair die fair die and a not fair die not fair probability of 1 would be 0.5 out of 6, probability of 2 would be 0.5 out of 6, 0.5 out of 6, right? And then the probability of these guys would be 1.5 out of 6, 1.5 out of 6, 1.5 out of 6, okay? The total is still 6 out of 6, which is 1, right? Yeah. But it's not balance, it's not fair. You can have systems like this. Let me read, make sure I'm going on the right road. An example of this would be, you want the average, a grade for a student, but you have six quizzes and one, ah, perfect. That is exactly what we ended up doing. You'd weigh the final more, that is exactly it. I'm trying to figure out where I would use it, right? That's exactly where we use it. These streams make me want to learn more math. Awesome, awesome. See, it makes me realize how much I know and how much I'm utterly ignorant of at the same time. Me too, because I learn a lot from these guys, right? So this would be something that's not fair, right? Or you could think about it this way. These guys are weighed more than these guys, or these guys are more important than these guys. It doesn't apply to a fair dice because you're usually cheating if you're not trying to make the dice on a fair, but as a mask of Raven says, you could do it this way, right? Let's assume you're writing six tests, right? One, two, three, four, five, six tests in your class. I'm very good at basic math, but rusty in other areas. Yeah, I tell you choose me too, but my basic math sort of functions as well, right? The camera is not focusing. So let's assume you have six exams you're writing for the year, right? And let's assume exam number three, should we do six? Should we distribute this? No, yeah, let's do six. Let's assume exam number three is worth 25% of your mark, and exam number six is worth 30% of your mark, which is a possibility. The reason being is this could be your midterm if you're doing a class, right? So test number one, test number two, test number three is chapter three plus one and two. So it should be way more, right? Test number four, test number five are standalone chapters. Test number six would be the whole year, okay? And if you want to make the whole year, let's make this one 35%, make it worth a little bit more, right? So right now, this and this is 50, 60%, right? And you make every other test worth 10%. Okay, oops, 10%. 10% and 10%. Okay, the finals usually 40 depends. Some places, I've wrote exams where the finals actually 100% of your test. For me, it's actually 40, 60 and 100 depending. Yeah, should we make it 40? Let's make this 40. Let's make this 40 and make this 20. 20 and 40%, right? So let's assume, now all the test marks, they're not going to give you tests where this only has 10 questions, 10 questions, 20 questions, 10, 10, 40 questions. They could, right? They're really lazy about the calculation, right? But usually each chapter has their own types of questions they ask, right? So each one's going to be out of a different grade, different number of questions. So let's assume the first test had 30 questions. The second test had 40 questions. The midterm had 40 questions. This one had, let's say, 20 questions. This one had 20 questions. And the final, let's say, had 40 questions, okay? Let's assume on the first test, you got 20. On this test, you got 30. On this test, on the midterm, you kicked ass. You got 38. You studied hard, right? On this test, you were flying high. You didn't really feel like standing. You thought you knew it all. You failed it. You got 5 out of 20. Should have studied, should have studied, right? Let's assume you were totally destroyed, distraught. You were, oh, man, I can't believe I only got 5%. And you were really depressed and you didn't have the energy to work, but you'll work yourself up. You got 10 out of 20 here and you finally kicked into gear. You said, no, no, no, I gotta do well, I gotta do well. And you got 35 out of 40 on this one, right? Good job. So what you need to do now is figure out what percent each one of these is, right? So what you could do is figure out the percent here, which is, I should have picked numbers that came up better, but did these ones come up better? No, they don't. So we're just gonna do this, right? Oh, God, I'm gonna use a calculator. I don't want to use a calculator, but let's do it anyway. Let's use a calculator. Those are time factor. Yeah, we're good. Good, good, good, good. So this is basically 2 divided, well, this is 0.67, 0., let's write it as a percent. 67%. This is 75%. 38 out of 40, 38 divided, oops, 38 divided by 40 is 95%, right? 95%. This is 1 out of 4, so it's 25%. This is 50%. And 35 divided by 40 is 87.5%. Okay, now there's multiple ways you can do this. Figure out what your total grade is, right? You could standardize these, right? Put everything to the same weight, right? The other, that was a formula. I can't remember the formula for, there's a formula, like you don't really need to, but let me follow the, get the exact terminology. That way I'm not writing formulas that are silly with the variables all whacked. Maybe it was a formula. You got to do sigma notation and yeah, where is it? There it is. That's the one we want. Is it? Statistics made easy. What? It doesn't look like familiar to me. That's the one I want. Yeah. Is the weighted mean? Here we go. Is the allocated weighted value is the observed value? Okay. So this is one formula. I hope this is the correct. This doesn't seem like W. Is W what we use? Yeah. There's a lot of formulas saying it's W. Okay. We're going to use W. Okay. So weighted mean is this. Let me bring out the chat so I know if there's anything being said. Isn't the sum of each percentage multiplied by the weight? Yeah. Yeah. Okay. So basically the formula is this. Let me write down the formula. It's x weighted. Right? Is the sum of that times that divided by the sum of the weighted. Is it i? What is that t? Gotta get a better. Yeah, it's t that they're using. t. Okay. It's blurry. Oh, here's another one. I'd like this one. Number of periods. No, that's not it. This is the one. Okay. Oh, I like this one better. Sum of that. Oh, that's just the average. That's not the weighted average. Here it is. W. Do you know what I mean? You need these sub things in there. Okay. Well, you do sort of, you need the sum. You need to do it. All right. So basically, let me bring this up. I say, I say we don't want to get those statistics and stuff and people bring up statistics hilarious. So the sum of this thing, this basically becomes this, right? So you multiply them and add them, right? So what do you multiply? You're going to figure out how we're going to do this. This is better out of 70%, 10. Yeah, you could do it this way. How should we do it gang? Should we go 67 times 10? Because that's the percent that is worth, right? So we could do it this way. It should be able to anyway. Correct me if I'm wrong. So the average, the student got was 75.7% by Michael because let's check it out. So what you would do is you would go 67. I shouldn't put that somewhere. 67% and that's worth 10% of your mark, right? So if it was 10% of the mark, this whole thing added up adds up to 100% of your mark, right? So what you could do, you could consider 10% to be 10 marks, right? So what you would do, you would go the average for this would be 60.67 times 10, 0.67 times 10, plus 0.75 times, let's just put these in brackets, times 10, and then plus 0.95 times 20 and so on and so forth to 0.875 times 40. All of it divided by the weight, which is 100 I guess, right? I got 66. I didn't say 67. I better, I guess I better do mine, right? Let's check it out. Well, that's 0.67. That's 0.75. 0.95 times 20 is going to be 19. So this one's going to be 6.7. That one is 7.5. That one's going to be 19. This one's going to be 2.5. This one's going to be 5 and that one's going to be 0.875 times 40 to 35. Oh, what am I doing? Oh, yeah, 40%. That's right. Oh, yeah, I made it out of 40. That's why I made it easy, but that's a mean calculation. So this isn't weighted mean? 0.67 plus 7.5 plus 19 plus 2.5 plus 35. So I got 75.7. Yeah, 75.7. I got the same number as mask of Raven. So if you do this, you end up, and this is over 100 because the total is over 100, the WT, the weighted, whatever the percent you got. I don't know if it's weighted. What do they call this? I don't know. What do they refer to? Particular weight of a certain thing. So it's the weight of that guy. So you do this, you get 75.7%. That's the weighted average. If you didn't do a weighted average, you wouldn't get the right number because you would just add all this up and divide by 6. So if you didn't do a weighted average, I said if you thought, oh, 67% here had the same value, it was 87% over there, had the same value as 25%. This would be 0.67. Oops. 0.67 plus 0.75 plus 0.95 plus, I don't even need to do 0.5, but I am plus 0.5 plus 87.5 equals this, and then divide by 6. Divide by 6? Oh, what am I doing? No, divide by, oh, what? No, ah, jeez, what am I doing? Yeah, yeah, the average, she's sending me 67 plus 75 plus 95 plus 25, because my calculator, I punched in something wrong. 50 plus 87.5. Yeah, that's better. Divide it by 6. I was getting Waco numbers. If you didn't do a weighted average, that means your number, your percent was 66.6%, which is inaccurate. Mask wins, mask wins. For what age group is this math in? I don't know, one day, in my part of the world, they used to teach it in grade 12 math. That's one of the reasons I learned this stuff many years ago. Well, I learned it when I was going to university, but I forgot it and I relearned it, right? But unfortunately, in my part of the world, they took this out of the math curriculum, the basic pre-calculus math curriculum. They're now reintroducing it, they're bringing in just this year, they're introducing statistics classes and I'm telling my students to take those classes because it's really important, right? But for me, for the last 10 years, I haven't had the opportunity to teach this because they took it out of the curriculum. Just imagine, they took statistics out of the curriculum. One of the most important things you need to learn in mathematics to be able to function within our society, they took it out of the math curriculum in high school, insanity, right? Insanity. So, if you didn't do a weighted average, you got 66.6% average. If you did do a weighted average, you got 65.7% average, which is way better. This would be appropriate for anyone who knows how to multiply and deal with basic data. I don't know what age that would be. Yeah, basically, master agreement that is 100% correct. And you have to understand how to analyze systems, right? Why it is that you're doing this. But yeah, all you need is addition, subtraction, multiplication, division and understand what percentages are. Okay, I can't believe we think only high schoolers can do this. Yeah, I stopped going after ninth grade. I started my business and then I sold it. Good, I'm glad. I hope you did well. But this is good to know. Maybe you could have sold your business for a lot more if you knew this. Maybe, maybe, or decided not to sell the one. Wow, look at what's going on. I could do, I could take it to the moon, right? I could take it to the moon. Fun. This may be a very vague question and off topic, but I have a desire to pursue a degree in mathematics. Which type of math degree should I go into for the most prospects in the future stats? No, let me rephrase that. Electrical engineering is huge. And if you do math, you can go into electrical engineering. You can go into any type of engineering in general. But when it comes to let me rephrase, I don't want to direct you down the wrong path. There's a lot of different branches of mathematics. Okay, there's a lot of different branches of mathematics. But statistics is one place that's used in many different fields, many different fields. Okay, maybe insurance companies, maybe governments, maybe corporations, maybe local communities trying to figure out what their community is involved in, what they want to do to to everywhere. Statistics has very, very deep tentacles within our society. So this would maybe have the most doors, most options for you. Maybe. There might be other people that might know a little bit more. Programming is huge, of course, but you have to be willing to code. Anyone see the movie 23? Yeah, I saw that movie. I liked it. It was fun. He starts doing math on everything and always end up with the number 23. The end, and it drives him nuts. Yeah, there's a lot of mathematicians that have gone crazy. Not that Jim, I don't think Jim Carrey was my petition. I can't remember. But we're human beings, our men and we mentioned this earlier in the stream. Human beings, we're pattern recognition machines. We're so good at it, we find patterns where there are no patterns. And if you don't correct your mistake, you will go crazy. My b i l is a software engineer analysis, any major in math and taught himself Java. Nice. Yeah, once if you learn math, you can teach yourself anything and any English in English or any natural language you have. But if you have a math core base understanding, you can literally learn anything. If you put your mind to it, statistics, number theory, specializing in photography, lots of types of applied math, computer sciences, very mathematical, steady algorithms, financial math is also good. Yeah. And all financial math to statistics is a huge part of that. Right. Yes, I was interested in becoming a data analysis. Yeah, data analysis is I love data personally. We are programmed to find patterns in order to try and understand them. Yeah, it's self preservation too. Right. If you're back in hundreds of thousands of years ago, right, even animals do mathematics, statistics, right. If an animal, you know, if a tribe eats a certain type of food and most of, you know, whoever eats that food gets sick. That's math, math, math, mathematics, pattern recognition. People go, oh, that food is not good. Don't eat it. You die. Right. It's self preservation. Need more math and movies. Need more math and movies. I agree. And good math, man. I've seen some movies that have horrendous math in them. I look at them, I go, what? Happy Friday, Zara. Happy Friday, brother. Happy Friday. I gotta pop a cuckoo. Oh, I can't pop a cuckoo. My fingers are all dry, racy. So I don't want to eat that stuff. I can't touch it. I should have brought a fork to eat my cuckoos. Actorias make a lot of money. That's in, that is stats. Yeah. Actorias is huge. Almost two hours. Are we having live streaming? Yeah, we have been. Cool. Fun, fun, fun. One problem I find with today's schools, we don't educate them. Nope. We make the kids learn what we want them to know and we make them fear what we don't want them to know. If you let a kid play around with coding for PC and programs, this kid will be a genius at the age of 12. 100% agree. The potential in each individual is almost limitless, but we don't nourish that potential. 100% agree. Welcome to our streams, brother or sister, right? That is actually one of the main theses of the work I do. I've been producing for the last, I don't know how long, 14 years. Why not go beyond two hours? Why not go beyond? I lose my voice a little bit. I do, I do streams with students and in person. So there's only a certain amount of talking I can do in the summertime. We might Hannah, but right now, my energy level just dictates two hours and I like the two hour session. It allows me to do other things. And I really want to, you know, get back into hardcore editing videos as well. I know I haven't been putting out too many editing videos just because I'm busy at work, it's the end of the school year and I'm doing the live streams and stuff, but that's one of the reasons Hannah. But we will at some point do marathon streams 100%. There's an excellent winning Gibson novel called pattern recognition. Ah, cool. Very true. But then you're in the insurance industry. Very lucrative industry though. Could I use a math degree to become an electrical engineer or would a physics degree be more useful? Depending on what type of electrical engineer I've known people that have gotten their PhD in electrical engineering. A lot of the books that you saw that you might have seen when I'm showing you my book collection, they're basically specifically electrical engineering books, but it's not physics, they're mathematics. So electrical engineer, I believe if you're going hardcore electrical engineering, mathematics is the core you want to learn, not physics. But people can correct me on that. It's mathematics you want. An engineering degree would be appropriate here. You'd be dealing with specific math concepts there. An electrical engineering degree would probably be best for electrical engineering. Yeah, true electrical engineering degree. But that being said, I've known people that got math degrees that have gone into the electrical engineering department and gotten their PhDs. Okay. And they were hardcore math. So can you do a stream on medicinal herbs? We've done Hannah, we've done three streams so far on entheogens. And we can again. I know Eduardo really likes them and some other people really like them. Right. Makes sense. Who will win the Greek Cup? I don't know. I don't follow the sports very much. Heavy math and electrical engineering also should probably know a lot regarding the physics of electricity. To a certain degree, mask off, mask off Raven, right? Depending on if you're doing coding, what do you call it? Not coding. Dealing with prime numbers a lot and security. If you're dealing with security and communication and stuff like this, that's electrical engineering, but communication, but very little to do with electricity. It's about the mathematics behind it, right? Isn't physics an application of math? Yeah, basically. Math is numbers, electricity is numbers. If you are good with numbers, you're good with pretty much everything that involves basic math, like building houses, landscaping, plumbing, and so on. Yeah. It also involves a bit of calculations. Radishes grew so fast it's your 1.5 weeks and they were popping up, tasted amazing the salad. Yeah, nice. I've been getting some radishes, Hannah, from the CSA we belong to. So they started giving us radishes for the last couple of weeks. And I'm assuming today we're going to pick up another batch as well. So I'm assuming we're going to have radishes again. And they're amazing. They're really delicious right now. They're radishes. And we use the radish tops and the cuckoo we made in this thing we made during the live stream on Monday, right? It's got radish tops and there's a supermarket. Don't forget the garlic. Oh, garlic. I want to start growing garlic. I am still hoping for another cliff diving video. Oh, me too, Martin. Me too, me too. Maybe this summer if I get a chance to go cliff jumping. Very healthy and very good. I suck so badly at physics before I learned my math. And now so much interesting and cool with the background knowledge. Yeah. How much is the CSA? How much do you get a week? We paid 500. We paid 250 at the beginning of the season. We're going to pay another 250 halfway through the season. And at the beginning, we're not getting very much. We're getting like a big salad bag. We're getting radishes. We got eggs. We're getting half a dozen eggs. And we got something else last week too. So we got four different things last week, which isn't very much. But starting in about a month, we're going to get a lot more salad. Oh, we got kale as well last week. We get kale. We got greens. We get herbs. We get eggs. We get radishes. We got root vegetables and stuff. So it's pretty good. I'll show you guys what some of my CSA hauls are once we start getting more. Do you grow your own vegetables? Right now, not my own vegetables. We grow our own herbs, some of them. We have lots of mint. We have rosemary. We don't have parsley and stuff set up. We just haven't set them up. But I do somehow have some other herbs that we're growing. Don't forget, let's do token eight. Oh, token eight is eating during the summer. Yeah, that's right. Sorry. Thanks for the reminder. Remind me again. During the summer, we do. We'll set out on the patio. I'm in the process of fixing up the patio right now. Spring cleaning, fixing our patio. We had bugs on our plants, indoor plants. I've been trimming cuttings. I've got things in cuttings and killed a lot of bugs by hand and spray. So we're rearranging our plants. That took a lot of time. So we'll sit down in the patio and do an A to Z reading of token. But remind me again for sure, man. Do you find it worth? It's worth it? Or is it a bit pricey? It used to be a little bit pricey here, but prices have gone up for vegetables, greens. It's pretty much at par with everything else. Sometimes it's good. Sometimes it's a little bit more. But it's at par with what we would be spending on vegetables. But they're local. They're organic. They're taste phenomenal. We're supporting the community. And just the whole ritual of every week going there and getting your vegetables. And they grow other things. So we go inside the farm and look at different things that they're growing. We can buy tomato plants there. It's worth it. It's worth it. Definitely worth it. Way better than walking to a grocery store and buying things. And the eggs are like two days old eggs. The vegetables are picked like a day or two days before. There's zero transportation. So other than us going there, sometimes riding our bikes to get there, you get the stuff right. So it's phenomenal. This Wednesday, we will be victorious, as Martin says. Did you hear the European Union new law about selling eggs? They made it legal for stores markets to sell eggs that is seven days before the expiration date. So now the world needs to throw more food and waste even more crazy. Or you got sale, lots of sales. Just go buy lots of eggs and make lots of cuckoo. Crazy. Crazy. Oh my God. Captain Picard with a beer. That's right. Make it so number one. How does four year transform? Oh my God. Four year transform. I actually, for my thesis, match this thesis, I use four year transform, but I can't tell you right now. I would have to look that stuff up hardcore. Hardcore. Don't waste food. My local Tesco sends out of date food to YMCA and hostels in there. Nice. Nice. That's good. Candy players. Glad you like. Glad you like, man. Give me the cuckoo. Give me the cuckoo. I gotta, I'm gonna eat some cuckoo as soon as we finish this stream. I gotta go wash my hands. I should have brought a fork. Right? I gotta have some cuckoo. We got like three, four more of these left we're going to eat today with salad and stuff. It's going to be delicious. Fun gang. That was a good stream. We started out politics and stuff. We got into mathematics. That was fantastic. So I'll definitely load this on YouTube. The first part was politics, economics, politics. I try not to load on too much politics on YouTube because the algorithms are kicking in and my view counts are going down because I'm talking politics. I'm not politically correct. I refuse to buy into the BS, right? But I'm cuckoo for cuckoo. I'm cuckoo for cuckoo. But we did a fair bit of mathematics. So I will definitely load this on YouTube and bitch it. In Sweden, the stores throw it in the bin and then trashman comes and picks it up and throws it away. Some people have started dumpster diving. They get inside the dumpsters and take as much food as they can, but that's illegal. Yeah, same here. It's illegal in my part too. That's why I think there's a law where they have to lock their dumpsters. If they don't lock it, they can be fined and stuff like this. And I don't know, crazy. Tomorrow at 8 a.m. Pacific time. Tomorrow, 8 a.m. Pacific time. We do a live stream on current events. I'm so bored at work. Oh, Hannah, you forgot your tea today. No, I brought a tea. I just been talking a lot. So I've been drinking. Even though it's gotten cold, so I can pound it back. Even though Twitch keeps on saying I should be drinking more water. The world needs more chichos and more cuckoos. Thanks for the love, Neil. Thanks for the love. I'll keep it going for as long as I can. I'll keep it going for as long as I can. And thank you for the support, Neil, for the donation and stuff. Okay. Okay, gang, we'll call the stream tomorrow morning at 8 a.m. Current events, 8 to 10 a.m. We're going to do current events. And next week, again, for sure, we'll do one math and one current events. And I'll try to slip in more live streams mid next week, not this week, but mid next week as well. Okay, we'll see what we can end up doing. Maybe a food stream in there somewhere. Any vacations planned for the summer trip? No. I might go to music events, if I can. But I really have a lot of work that I want to do for the content we're creating here. Hannah, I got math stuff that I've laid out that I would love to get to. I just need to get to. 8 a.m. Los Angeles time, Martin. Yeah, 8 a.m. Los Angeles time. Current events tomorrow morning. Okay. Aside from that, gang, thanks for being here. Thanks for the questions. Thank you for the answers. Thank you for the information, providing information that we didn't know. I didn't know. You know, some of you didn't know here. It's a great avenue to share information and help each other out, right? And if you can make it, I'll see you guys tomorrow morning at 8 a.m. Okay. Bye for now. I hope you have a fantastic Friday and a fantastic weekend. See you guys in the next stream, gang. See these are right here. Thank you for the time. Sampeh, Sampeh. All right, see you guys. Good stream. Take care, Chucho. You too. You too. Perfect. It'll be up tomorrow on Bitshoot and YouTube, brother. So you can check it there. Okay. Bye for now.