 and share the tables. So let me look at this one. The one with four digits, okay, that's correct. So welcome to the final exam prep before a day before you write. So the if before you write your exam out of the way, your exam split into two sections. Session number one and session two. Session one, like with the assignment where you had assignment one concentrating on a couple of questions and chapters and assignment two looking at different chapters. You will also do the same with your exam. It's split into two so that it gives you enough time to also go for a toilet break or a breather or go from, I think nine o'clock or eight o'clock. I can't even remember, I think from nine o'clock until one o'clock. So you can take your exam any time between those time. So your time will close or your exam will close off after one o'clock. So what happens when you start your exam paper? Please check first your load sharing schedule. We know that Escom these days is back with black out. So please check that that you don't have any load sharing. If you have load sharing during that period between nine and 11, look at the times pace yourself because one session it's about 75 minutes. So it means if it's one hour 15, one hour 25 minutes or one hour 30 minutes, something like that because it's 75 minutes, one hour 45 or something like that 15 minutes. So pace yourself in a way that you start your exam two hours before load sharing, and then you wait for the load sharing and make sure that your load sharing doesn't end at one o'clock. Wait for the load sharing and then when the load sharing is done start another paper. So you can start your exam like I said any time between nine and one. So you can even if there is no load sharing, you can start your exam by 12 o'clock, but make sure that you not by 12 o'clock because then you will be late because you only have one hour. So you need to make sure that by 12 o'clock you already have started at least one of the sessions. The other thing you can start any session anyway and how you want because there are two independent sessions. One does not influence the other one. So you can start with session number two and get over done with it because it's got questions that or chapters that you feel you are comfortable with or you can start with session number one. The way you start your sessions, it's up to you. OK, number two, please make sure that it's an open book. Open book means you can bring any material, anything you want. So there's no need for me to even skinner and say, oh, don't tell anybody that. So it's an open book. It means you can bring your study guide. You can bring your question papers, your past question paper, your mock exam papers, all those things. But be mindful that the more you go search for things, it might take more time away from doing the actual exam. What I will suggest you do today after we've done with this, take a breather and go back and summarize information, put things like make yourself a summary page where you know that study unit one, we cover one, two, three, four, five and have this and this and this. These are the formulas that are required for answering this kind of a question. Make notes for yourself and have that as your point of reference before you can go to your study guide to any other page in through the textbook and so forth. If you have that as one of your input, it will save you a whole lot of time because those are notes that you made. Summary notes that you made, you understand, and they will make your life easier. Number three, also tables, your lecturer set in that tutorial letter. You need to use your tables that were given in your tutorial letter or your study or some way, I can't even remember now which one, the tutorial letter one to one. If you have tables, use those. Otherwise, there is a documentation that we have been using during our classes that I shared with you. It's got formulas and also it's got tables and we're going to use it today as well. Use that as your reference tables for tables so that you don't have to use a different table with three decimals or two decimals so that you standardize your things. I use the one with four decimals. That is all in terms of your exam. There's nothing more. There's nothing less. The only thing that you need to do during your exam is just take a breath, relax, and tell yourself, I can do this. Do not panic. Do not go into a panic mode when you can answer question number one. Say, ah, that's easy. Which whatever goes goes and then you answer your question paper. And that's all from me. So now let's go into it. Let's start looking at the mock exam paper. I thought we can look at any other exam paper, but we're going to just look at the mock exam paper. Guest, you can unmute. Good day everyone. It's just going back to the exam itself. Will it be a linear exam where you have to answer a question before you move to the next one? Yeah. Can you hear me? Yes. Yes. I think I got lost like a network. Yes, I do. Wow. It's been challenging. Yes. Okay. Can you repeat your question or I didn't hear that? So I was asking about the exam itself. That will it be a linear exam where if you skip a question, you can't go back? I think so. The same format as your assignment. So it means once you answer the question, you just move on the same way. So yeah, it will be a linear. You can't go back to the once you skip two, you need to answer that question. Okay. Thank you. No problem. Okay. Are you able to see my screen? Yes. Okay. So no problem. And then we can touch. With question number one, without wasting any time, because we only have two hours to do the rest, to do all of them. Which one of the following statement is incorrect with regard to a statistic? So I assume at this point you all have read, you all have revised. Is it A, B, C, or D, or E? Statistic. I'm not sure if you are using the chat, if you are using the chat, also using the chat. Somebody also posted the tables on there. So you can also, if you don't have a copy of the tables, you can use that. If you're using the chat to communicate with me, I will have to join on my phone as well, so I can see the chat. I think the answer is B. So we have B, and on the chat we have D, B, C. Okay. So a statistic, sorry. I was still busy trying to get to my, let's give me a sec, to my chat. Okay. So you must also remember what a statistic is. A statistic is a measure that comes from a sample, right? Those are measures that comes from a sample. A says a statistic is a summary measure calculated from a sample. We're looking for the incorrect one, and that is correct. Number B says a statistic is not an estimate of a population. It says not, because we know that a sample statistic, we can use it as a point estimate to estimate the value of a parameter, and that we use it in the confidence interval. Remember that? So for the fact that they say not, that makes that statement not correct, because we know that a statistic is, it is an estimate of a population parameter. C says a statistic represents the property of a sample that is correct. A sample statistic or a sample mean, which is your X bar, is a statistic. It is a measure that we calculate from the sample. A sample standard deviation is also a statistic, which is your S. Okay. So the only incorrect answer here is B. So you need to remember that. From a population, we get a parameter. From a sample, we get a statistic. Question number two, information on the following variable is gathered amid COVID global pandemic. Which one of the following statement is incorrect? A, the medical cost of each patient in rent is a quantitative continuous variable. Remember? Yeah, we're talking about variables. So you need to remember that quantitative variables can be counted or measured. If they are counted, they are continuous. Sorry, if they are counted, they are discrete. If they are measured, they are continuous. So you need to remember that. We also have qualitative variables, which are variables that you can place in two categories. So now it says the medical cost. The most important thing is that the medical cost of each patient in rent. That's the statement you need to evaluate. Whether is it a quantitative or is it a qualitative? And we're looking for the incorrect one. The name on the list of the province affected by COVID-19 is a qualitative nominal. Name or list of provinces, that is what you need to evaluate. Is it qualitative or quantitative? And because also they mentioned nominal, you need to also remember them. For qualitative, the scales of measurement or levels of measurement, we have nominal where there is no order or preference or levels. And we also have what we call an ordinal where there is order or rank. So you need to check whether that statement, is it nominal? The severity of a symptom, whether it's mild, moderate or severe, is a qualitative nominal variable, like I explained. So you just need to look at actually what is inside the bracket. It's most important to evaluate. Common COVID-19 symptoms such as cough, fever, tiredness, shortness of breath is a qualitative nominal. Also the same under there. Sorry, are you asking a question? You just need to check the information in the bracket. It will give you guidance in terms of how to answer that question. E, the number of confirmed COVID-19 cases is a quantitative discrete variable. A, B, C, D or E. Which one is incorrect? I say it's C because isn't it supposed to be ordinal variable instead of nominal? You say it is C. Yes. C because it's supposed to be ordinal, not nominal. Yes. C because that information there, it should be, the answer here, that should be ordinal. The total number of COVID-19 confirmed cases. Can I ask a question? Yes. On that question that we just passed, number A is just, I'm a bit confused because I thought it was A. Is it, can we count, can we count that number A? What is it saying? Is it a medical cost? Yeah. So it's not discrete, not continuous because, can we measure, sorry, we can count but not measure? No. You can't count. Okay. So what do you need to also remember? Yes. What you also need to remember is, in terms of continuous, it is those questions that you can ask by how much? How much and discrete you can ask, answer by how many? So that should give you a guidance. Continuous, much. I hope my continuous, I wrote it correctly. Conti, it's got another U somewhere that I'm missing. Continuous and discrete, we answer. So those should be your guidance in terms of how to determine also which one is a continuous and which one is a discrete. Right? Moving on to the next one. So we are given a frequency table with the provincial breakdown. We need to answer the following question and choose which one is incorrect. A says the percentage frequency of umpumalanga. How do we calculate the percentage frequency by taking the value? So this 37 divided by the total number multiplied by 100. So that will be your percentage frequency. You say 37 divided by 15, 5, 1, 5, multiply the answer by 100. That will give you a percentage frequency. So you need to do the percentage frequency from umalanga, which is 71. The frequency of notary and cape, which is this are your frequency. The actual values they gave you, which they say the number of. They can also put it as a count. Those are your frequencies. So if you look at notary and cape, which is notary and cape is the first one. Is the frequency of notary and cape 37. We're looking for the incorrect one. Always bear that in mind. The relative frequency of how thing. So relative frequency. I'm going to write it this site relative frequency is the same as your percentage frequency, but relative frequency. So let's say for notary and cape, it will be 37 divide by 15, 5, 1, 5. That is your relative frequency. So you go to how thing was how thing. You take that value divide by the total that will give you your relative frequency. The frequency of Northwest. So remember frequency is that column. So you go to Northwest and you look at the frequency of Northwest is that the frequency of Northwest. The relative frequency of Eastern Cape. You go Eastern Cape. You take the value of Eastern Cape, which is one nine. 36 divide by 1, 5, 5, 1, 5. And that will give you your relative frequency. So the difference between relative frequency and frequency percentage percentage is your relative frequency multiplied by a hundred. If you look at the notes, we also have. An example of that a b c d. D. D is the incorrect statement because the frequency of Northwest is equals to 70. So that should be 70. I can see if you raise your hand. If you want to say anything, you just let me know. Okay, given the data below, it shows the stem and leaf plot of daily COVID-19 cases during the second week of the national or the nationwide lockdown. Now we need to use this information to answer question number three to question five. You must always remember with your stem and leaf plot, you need to know how to read your stem and leaf plot. Remember the values you see on the stem and leaf. The first digit before the line, this are what you call the stem and this are your leave. There is one stem and many leaves. So this value is not one, but that is 31 and this value is 43 and that is 63 and so forth. 63 and so forth until you get to 96. So that's how you read this table. So in order for you to answer the questions, you need to decipher this table or this stem and leaf plot by doing it that way. So I'm going to give you some time to think about which one is correct. So remember a symmetric means the mean is equals to the median. That's symmetric. The mode refers to the most frequent or the number that appears more than the other numbers. So it means the number that is repeating more than the other numbers. So for example, if they had another zero there and another zero there, then it means 70 repeats more than the other numbers. So that's what we are referring to there. The range is your highest value minus your lowest value. The mean is the sum of all your values divided by how many they are. The median, you can go and find the median position by using n plus 1 divided by 2. And then using that to go find your median. I'm going to give you some time just to work through it. I will be back. Have you all thought about it? Have you got your answer? A, B, C, D, O, E. A, A, A. The data is not symmetric. The other thing you can also use to identify, symmetric will mean that probably this line would have been somewhere in the middle. But that is also not in the middle. So that your stem and leaf plot would look like normally distributed like that. The moment you can see that it has a tail 2. This one. We can draw a normal distribution like that. You can see that the tail is to the left. So A is the incorrect statement. The next question also asks about the same stem and leaf plot, but now we need to do the quartiles. Remember, quartile 3, we use 3 times n plus 1. Divide by 4. Quartile 2, n plus 1, divide by 2. And quartile 1, position. Remember, these are all positions. Quartile 1, position, we use n plus 1, divide by 4. Or you can use 75%. So this is 75% times n plus 1. This is 50% times n plus 1. So some people prefer to use 0.75 times n plus 1 and 0.5 times n plus 1 or 0.25 times n plus 1. You can use the percentile or you can use the quartile formula. This we will find the position. So you must read your question correctly and carefully. Because in your question it says the value. Let's see. Interquartile and value, yes. It's your screen still shift because I can't see you. You don't hear me. No, I can't see you. You can't see me. Yes. I can't see you. Yeah, I'm good. Oh my goodness. I can't see the screen. I can't see. I think it's back now because I also couldn't see, but it's back. I can see. Oh. All right. So this is value position, position interquartile range. So this is to find the position. The answer you get when you find the position and the answer is 0.5. Then remember to take the average of the two values that both of them are located between. If the answer here is 1.5, you go find the average between the value between 31 and 43. So you go and say 31 plus 43 and you divide by 2. That is if the answer is 1.5. So you take an average if the value is 0.5. Now, if the value you go into round it down, like we do with the normal rounding up and rounding down. So that will round down. So if the answer was 1.25, you just round it down to 1. So then it will be 31. So if the answer is 0.75, then we round up. So if it's 1.75, therefore our quartile value will be on position 2. So you just need to remember all that when you answer the quartiles. I don't want to remove all of them. I only want to remove these ones that I just wrote. So you need to go and find the position for quartile 3 by using that position value. You need to go find. You've gone Miss Lizzie. Position, sorry, calculated the position, then you can go find the value. Inter quartile range is your Q3 value minus your Q1 value. That's the incorrect one. Time to work through it if you haven't. Your communication is just breaking up every now and then. I think my network is bad. Hello. I can still hear you. I think it's maybe Lizzie. Yeah, I think so too. OK, just making sure. Am I now audible? Yes, yes, yes. Yes, you are. All right. OK, so let's. Do you have an answer or are you still working out? The answer is D. The answer is D. So what is the value of Quartile 3? It's actually 46. Is 46. Inter quartile range is 46. Inter quartile range is 46. OK. So the answer here is D. Sorry, can I just ask a question? Yes, you can. So you're doing the inter quartile range. It's based on the position. It's based on the value, not the position. Yes. OK. Yes. And then how do you find like the value? Because I'm having struggling. The position. OK. Not the value. I think. No, the position. Yeah. OK, so let's let's find the position. So you did say three times N plus one. Divide by four. You say three times seven plus one. Divide by four, which is eight times three. Divide by four. What is the answer you get there? Six. Six. Is it six? Yes, it's six. Yeah. Then you go count. So don't count this values yet. Just count the values, the leaves. So say one, two, three, four, five. But you must also count this value because it's also a position. Six. So then when you read this, you say 89. So the value is 89. OK. OK. Because this is a stem and leaf plot. Remember? Like we did here. I said when you read this value, you say 31. Like we deciphered it. Yeah. This is the one for the three. So this is 89. It's on position. Six. Don't come from here and then start from this side and go there. Start from the smallest value and go up to the highest values. OK. So that is how we found quarter three. And you also need to find the quarter four value. So if there's two values are correct. Therefore, this was 89 minus 43, which is 46. Thank you. That's why it makes that. OK. Moving on to the next one. Consider a stem and leaf plot. Also, we still on the stem and leaf plot. Now on this one, you will have to decipher this information and capture the information and calculate the values. You will need to calculate the standard deviation because they say the mean is 67.43. What is the coefficient of variation? So a coefficient of variation is your standard deviation divided by the mean multiplied by 100. You are given the mean, but you are not given the standard deviation. So you need to go and calculate the standard deviation. Now, you can either use your calculator and take your calculator to state mode. I hope by now you know how to do that. Or otherwise you have to use your formula, which is the square root of your variance, which is the sum of your observation minus the mean squared divided by n minus 1. So if you use the formula, since I don't have my calculator and my trial version of my calculator is finished, so I don't have money to buy. So you just need to say the mean they gave you. So you will say 61 minus 67.43. And then you'll say squared plus. And you go to the next one. 43 minus 67.43 squared plus. Plus until you get to 96 minus 67.43 squared divided by. Oh, I must not forget the square root. Divide by 7, 7 minus 1. Otherwise you can use an Excel if you don't, if you don't have a calculator, since we always use Excel to assist in the exam as well, you can also use your Excel. But I will prefer you to use your calculator to save time because if you have created the templates for yourselves and then you can use them. And if you're going to use templates, you need to know how to operate the templates because then sometimes they are not straight forward. There are things that you need to adjust when you use your templates. Please kindly share how to do it on a calculator. What calculator do you have? I have a Casio scientific calculator. Okay. On your Casio calculator, you go to mode and then you will press the number that corresponds to what you see. G-C-S-T-A-T stat. Yes. What number is that? It's two. So you will press mode and then press two and what else do you see? There should be one that says one var. Yeah, one var. It's number one. You press that number which is one and you will have a table and a table that will have an X column. Sometimes the table will have a frequency there. You can just ignore the frequency. We're only looking for the X. Now, you're going to capture the value by saying 31 equal. When you press 31 equal, oh, sorry. When you press 31 equal, it will put 31 there and then you go to the next one for the 3 equal. It will place it on the table. 63 equal. It will put there and you complete the whole table. 80 equal, 89 equal, 96 equal. Do all of them until you get seven of them on there. Once you have all of them. OK, up to 96 is. OK, now you are ready to calculate your state functions. So it's very difficult to use a pen on. So now you need to press the AC button which is just to get your calculator. You will press that. OK, let's go back to normal. Now you need to press shift. OK. And then you will need to press button number one. On button number one, there is an STAT. Look at your calculator if it has that. On button number one. Yes, that's the button you press. Now you'll need to tell me what you see on your screen. I'm seeing one saying type two data, three, some four variants and five minutes. The one that says var, that's one that's the one that we are looking for. So you will press four for var. And you will see there will be in the mean. You need to look for the one that has an X. An S and an X. That looks like that. That is the standard deviation that we're going to be using. So on your calculator. You just press the number that corresponds with that. Give me that number. It's four. Divide by six seven point four three. Multiply by a hundred. Sorry, you said the number that I'm getting the SX number is twenty three point seven six. Okay. Twenty three point seven six. Yes, that's the one that I'm looking for. So that's how it is. Twenty three point seven seven divide by sixty seven point four three multiplied equal. So say twenty three point seven seven. Divide by sixty seven point four three. Equal multiplied by a hundred. Equal. What is the answer? Eighty five point two five. Thank you. No worries. Anyone who wants to take up? Sorry, Lizzie. Can I just ask you to repeat? What do we press after we have the SX that says twenty three point seven six? What do we do after that? No, that's the answer we're looking for. Remember your S. S is the SX on your calculator. And you just take that value and you substitute. Otherwise, since because I'm not sure what your X by is when you calculate on using your calculator. You can say where are you at now? Let me remove all this weakings. You can say after you can say shift one. Four. No, is it four? Yes. Four and four again. And say divide by. One. Four. What is the value that corresponds to X bar? Is it two or three? I think it's two. Quickly check. Go shift one four. And tell me what is the value that you see that corresponds to X bar? True. Is it two? And then press equal. And then once you have that multiplied by a hundred and then say equal, you should get the answer that we're getting. So this is from the calculator. So you will do it that way. I'm sorry, Miss Lizzie. Yep. I can't see the chats on my side because I joined with a guest account, but I'm getting the standard deviation of 22.01. I'm not sure if I'm the only one. Which, which, what did you use to calculate? I use the spreadsheet. You use the spreadsheet. Okay. So now I'm going to use the spreadsheet as well. So let me just do that because I've got all the values. Edit. These labels, it's grouped by column. Maybe I should, I should be sharing my screen. Yeah, Miss Lizzie, I was about to tell you. Just give me a sec. Okay. So on your Excel spreadsheet, I just need to double check if my values are correct. There are seven of them. Okay. So on your spreadsheet, you can have all your values. And depending on the type of a spreadsheet that you have. On my one, I do have an editing called the data analysis. I think when we did the regression as well, I showed you how to, to get that in. So by going to the file option, file options, and then you go to addings. And then you add your Excel, Excel editing. Okay. So it's an Excel editing and you go to the analysis tool pack and say, okay. And you select those analysis tool packs. You need to make sure you can select one, but I selected both of them. And then you click, okay. Then you need to restart your Excel sheet. And once you do that, when you go back to your Excel, the data analysis panel will appear under the data menu bar. You will have this section called the data analysis. So under the data analysis, you will capture your data. So you go to your data analysis after you've captured your data. Opens up this menu bar and you look on the menu bar. You will look for descriptive statistic. If we were doing regression line, the regression model will be there. But we're not interested in that. We're looking at descriptive statistic and you press okay. You need to put in your input values. Let me remove all these values that I have already. You go to your input value. You make sure that your cancer is flicking on the bar. Then you go and select the values. So if I select from X. I must also remember if I select from the label. I need to come and tick this. That says labels in my first row. So that it knows that I have selected labels in my first row. And I also need to tick one of them. Sometimes your data can be written in that manner. In the row manner starting from 31 from these columns. And my one is grouped under columns. So if you have any pop-ups open, we won't see them. You're clicking away. We don't see anything. You need to share your desktop. I don't want to share my desktop. You can hide all the stuff we don't want us to see. I'm fortunate that I made work. Okay, so you go to the file. Sorry. To add the data panel. File options. You go add-ins. Analysis tool pack. You click on the go. And you tick both of those. Analysis tool pack. And you click OK. Then you restart your Excel. You go out. You close this Excel and you open it again. Once you open the new Excel sheet, you come in. You capture the information as you want it. Sometimes you can take the same information and capture it in that manner. It doesn't matter how you've captured it. So you can do it that way or you can do it that way. And then you don't have to do anything. You go to the data panel. Data analysis. And you select descriptive statistic. Click OK. You're going to choose the values that you are using, including the label if you want. And you need to make sure that you tick the labels in the first row. You also need to tick where it says group by. So mine is grouped by column. If it's grouped by rows, then that will be grouped by rows. So we're doing the one that is grouped by columns. You also need to select the input output range. Also make sure that your line flicks inside the empty column there. And then you select any way where you want the output to be. You can also select the new worksheet or the new workbook. It will open a new one. A new worksheet, it will open another worksheet. A new workbook, it will open another Excel book. So I want my data and my report to be on the same page. So I just select any way inside this Excel sheet so that it creates where it will create the output. You also need to select the summary statistic so that we can have all the summary statistic. And then when you press OK, and there is your output. So this one is the one that I did earlier. You can just delete that. And you have your data. So you need to be very careful when you use this template as well. You will get two, you will get a standard deviation. And your sample variants and your standard era, your median and your mean, as you can see. So if I look at what we got, what did we say? We got 27, 23 points. So our CV, the previous one, because I removed all the values that I had, you had 23.77. Yes. Over the mean of 67.43. 43. Yeah. So if you look at the Excel output as well, and that is what we get, maybe I should go this way, 23.77. And the mean they gave us, but you can also get it from there as well. So that is how you can use an Excel, but let's not dwell too much on that. Otherwise you can use your calculator. You can use the formulas or you can even calculate it manually by applying the same thing. So by saying, we know that that is 31 minus 67.343 squared. And you just do the square. And you do the same. What am I missing? Oh, my comma. My comma needs to be a decimal point. And you can do the rest, the same as the rest. Sorry, my bad. I needed to change it to that. And we can have the sum, which will just be, I need to make it bigger so I can get my summation. Or to sum, that is my total. And I can take that total and calculate my deviation. I just taking the square root sqrt of this value divided by 7 minus 1. Or I could even set count minus 1. And that is my standard deviation weight. They didn't calculate correctly. So what am I missing? Double check something. You need to put the 7 minus 1 in brackets. Oh, yeah, you are right. That's the same mistake that I did. I noticed. Yes. That's correct. They need to be two closing brackets. Okay. And that's, you can see that I get the same answer as that. So this is the summation. If I put it that way. Okay, so you can use whatever, whatever you find at your disposal to help you. But don't dwell too much on technology and this and that. And then you can see that how long it took us. So you just need to make sure that you have prepared to use all this, all these tools if you want to use the tools. And you need to practice. You cannot use the tool when you get to the exam. And multiply by a hundred. Which did find that that was the answer. Okay. Moving on. We are still very far from finishing. Which one of the following statement is incorrect with regards to the experiments? Just give me some few minutes. It's such a gangsta ringtone. Just picked it up now. Okay. So this one, it's almost exactly the same as what you had in your assignment question. Which one of the following statement is incorrect? We have number of permutations of three items that can be selected from eight groups. Already they told you that that is permutation number of combinations. So it means you're going to use NPR to calculate the way your N is 56 and your P is three. So you know where to find that. You must look on your calculator for that function. If it's written in orange, you're going to use the shift button. So you will press five. Sorry, Liz. Yes. I think you substituted the 56. It's the wrong number. It's not N. The N is actually the eight. Oh, 56 is the number. Yes. Oh, sorry. The whole sentence. So that will be eight. Yes, you're right. That will be eight. This is the answer that you need to get. So you'll press eight. Second function and you go find that button that corresponds to the NPR. Three and that will give you your answer. Combination same for seven item. Out of five. Five items out of seven. So that will be seven C five. And this is what we call a combination question. You also do the same seven shift or seven second function depending on what calculator you are using. And go find that NCR button and then press five. And this is just, you need to know that the definition of probability, what is a probability? And the next one in an event with a four equally likelihood event. So you just need to know what is the probability of a simple event when you have four of them. So the probability of X will be, what will be that? What will be the probability of that outcome? Number five experiment with three steps. And four outcomes possible for each step. So yeah, also you need to find the number of ways that you can get those outcomes. And we are looking for the incorrect answer. The answer is A. A. The answer is A. What do you get when you calculate the permutation? 336. In the exam, you don't have to do all of them. When you get to the answer, you just move on. You don't have time to evaluate all the responses. Next. Yes. I would, can you do B? I don't know why I got 2520. B, you will say seven. Oh, okay. Okay, sorry, I used P, sorry. Consider the following below, which is the contingency table. Now with this question, you are given this contingency table and you are given decimals. So you need to know and remember when we talk about probabilities as well. So because this is probabilities, because I can see in the question, it asks questions about probabilities. You need to remember that when the statements or when in the statement you are given whole numbers like 20, 30, 70, 120. This we call whole numbers. We call them outcomes. These are events. So it means we can use these values to calculate the probabilities. When you are given decimals like this, these are already probabilities. So we can just use those probabilities to calculate. Sometimes they can give it to you as a percentage, which we call them proportions. As percentages in probabilities, when it's in a percentage format, we say it's a proportion. When they give it to you as a percentage, it's also probabilities because you just divide that percentage by 100 to get it to a decimal. So here you are given the probabilities. You just need to use these probabilities only for any formula that you need to be calculating. So let's look at the questions given. Find the probability that a caregiver works from home and their children is securely attached. Now, with this example or this question, they actually made your life easier because they gave you this in the bracket, which is what I wanted to write. The probability of home and secure, which is the joint probability. Therefore, we know these are joint probabilities from this. These are all joint probabilities. We know that we calculate joint probabilities there and we calculate simple probabilities from here. Now, before you even start answering questions like this as well, because you will require the total, I will suggest that every time you do answer the questions on probabilities, you write the totals. So you can quickly write this total. So this will be 6.5, which will be 0.5. So this is the same as the probability of secure, which is 0.56. That's how you will use the probabilities. So you need to complete this whole table. Do that before we can start answering the questions. And once you are done, let me know what values I must put on here so that we can work from the same common table. Are you done completing the table? Yes. Okay. You mean the values? Total for home would be 0.53. And total for home would be 0.47. Yes. And for insecure it's 0.44. Okay. So now we are ready to answer the question. Probability of home and secure. Look at the table. Joint probability. So this is probability of home and secure. They say it's 0.15. We are looking for the correct statement. Is that correct? No, that's wrong. Okay. The next one, we're looking for the probability of home and secure. Now on this one, you need to do a little bit of work. You need to write the equation of probability of home and secure is equals to the probability of home plus the probability of secure minus the probability of home and secure. So what is the probability of home? You told me that it's 0.53. Plus the probability of secure, which is 0.56. And the probability of home and secure is 0.38. Minus 0.38. Is that correct? It's wrong. That is also wrong. The next one, it says find the probability of home and secure. This is conditional probability. And for conditional probability, probability of home, given that it's secure, it's given by the probability of home and secure divided by the probability of a given, which is secure. Now you just need to go and find home and secure is 0.38. Divide by probability of secure is 0.56. And that is equals to 0.67. 0.67. So therefore this one is also not correct. The last one, oh, not the last one. The second last one, the probability of secure given that home. So also here we need to go find the same thing that we did with that one. We do the probability of secure, given home is the joint probability of secure and home. Oh, why am I writing the whole sentence now? And home divided by the probability of home. So we do the same probability of secure and home is 0.38. Probability of home is 0.53. 0.72. 0.72, so the correct answer is D. The last one, they wanted to just confirm the probability of home. Probability of home is 0.53. Which means that is not correct. Okay, that is probabilities. Also going to the next one. So the next one also deals with the same information, but now we need to find the incorrect statement. What is the event? Oh, so we need to find which one, which statement here is correct. The event is secure. The event secure and insecure are complements. Is secure and insecure complements? Yes. There are complements. It's like the same as the outcome of a coin. You had a head and a tail. A tail is a complement of a head and a head is a complement of a tail. That's the same scenario. The event home and away are mutually exclusive. Correct. Correct because you cannot be home and be away at the same time, so they are mutually exclusive. The event home and secure are independent. Now how do I know for independent events, the probability of home given secure should be equals to the probability of home? Or the probability of secure given home should be the same as the probability of secure. You can use either one of them to test that statement. Remember you did this previously. You have the probability of secure given home and also the probability of secure given home. Secure given home and home given secure. So let's use the secure given home, which is 0,72. Secure given home is 0,72. We need to make sure that it is the same as the probability of secure. The probability of secure is 0,56. Therefore, they are not the same, so they are not independent. If they were the same, we would say this statement states that they are, let me write it here. If they are the same, we would say they are independent events. Because we know for independent events, the given probability of secure given home, home doesn't have any bearing on what happens to secure, so it will be the same as the probability of secure. The same you can do with this one, which is home and secure. What did we get? 0,56. So the probability of home given secure is 0,56. And the probability of home is 0,53. They are not the same, yes? Just a quick question. When you're doing the independent and the dependent, where it says home and secure? So that's not the mutual, not the joint probability. Do you have to use the given probability to determine if it's dependent or independent? But these are not probabilities. Yeah, they're saying events home and events secure. So this you treat them as separate. Event home and event secure are not independent. It's not a joint probability. It's not a joint event. So can't you just then just say home and the probability of the 0.53 and just secure, which is 0.5 and then put them together to say if they are dependent or not independent? Nope, you can't do that because this statement needs to be correct for them to be independent. Oh, sorry. Here it's insecure, not secure. Actually, I answered question number D because I used secure, not insecure. So on this one as well, you just need to use insecure. Sorry, my bad. So we answered D, not C. Oh, okay. Sorry. Sorry about that. I'm going to get disturbed all the time because I'm still at work. I'm still in my work time. Okay. So thanks for pointing out that, but now I've realized as well that we are discussing the third one, which is secure, home and secure. So which is this one? So this is for D. So we've done D. So you can also do the same with home insecure. You need to go and say the probability of home given insecure, insecure should be the same as the probability of home. So you need to go and calculate the probability of a given home insecure. So which is the probability of home given insecure, which will be given by the probability of a joint of home. And now this is the joint event insecure divided by the probability of insecure. And then the probability of home and insecure is 0,15 divided by the probability of insecure, which is 0,44. So now, so to answer C. So we answer C with that one. So this one answer B. So what is the probability, which is 0,15 divided by 0,44? 0,34. 0,34. Which is 0,34. So we also do the same. So that is 0,34. Is it the same S? Nope. 0,53. They are not. So they are not independent. So that is correct. That's what we are looking for. Now D, home and secure should they say, the statement says they are independent. We also did find out that they are not independent. And that's how you can only answer this question when it comes to independent. Now, when it comes to the probability, because sometimes in the exam, they might not ask you the same questions like this exactly. You need to be very, very careful when you answer conditional probabilities as well. So for example, yeah, when we were answering conditional probability of secure and home, if the statement before that, where they say the probability that they charge, if they say, given, oh, if event, secure and home are independent. If the statements start with that saying, secure and home are independent. What is the probability that the child is secure given that they are at home? You need to remember to use the independent statement. So the probability of home given secure, you need to use this. So you can use the conditional probability. You can go and calculate this conditional probability. You will have to use the one for independent. Only if they tell you that the events are independent, then you use that one. Okay, now we're moving on. Left, the basic probability. So the other thing that you also need to be aware of is because you've got 25 questions and they are split into those sections. Every chapter might have two questions in the exam. So you will get 222. Like you can see here, we have two questions from basic probabilities. Actually, we had three questions from basic probabilities because also this one is from there. But usually questions are 22222222222. Okay, so next we're moving on to the next question, which talks to probabilities. Now, looking at this question that we have, we need to remember that after the basic probability, you go into discrete probabilities. And discrete probabilities has binomial probabilities. They also have a Poisson probability and the discrete probabilities. Now, this question is your binomial probability because they gave you the probability of success or the probability, the pi probability, and they also gave you your N. Remember also the signs. These are very important, very, very important when you answer probabilities. Greater than or equal, it is at least. Less than or equal, it is at most. So you will have to answer those questions like that. Equal is exactly, exactly. So what is the probability that at least 14 branches operated? So we know what our N is. So that is very important. You need to know your N. Your N is 20. You need to know your probability of success, which is 0,35. You need to know your sign. So now we need to go to the binomial distribution table and go and find out which one of the statements are incorrect. So 14 branches at least, we go to the binomial table. Remember the binomial table as well. It has the positive and, sorry, it has the top and the bottom side of the table. Remember where the small probabilities at the top, we use the left. The big probabilities at the bottom, which are this ones at the bottom, this ones at the bottom, we use the right. So this probabilities at the bottom, they will correspond to the N values on the right and the X values there. So now looking at the question that we have, we have N of 20. So we need to go to N of 20. So that is N of 20. There is this N of 20. I will need to turn the table around now again. So you need to be very careful as well, because I can see that the values here at the top are big numbers. So I need to turn it. So it's easy if you have it printed then online as well. So if you have a copy, a hard copy of, so we can use this site. We can use this site. We need to use the top and the bottom and the left. Please kindly repeat that. How do you decide which site to use? The smaller probabilities we use the left hand side. So we need to go to 0.35. We know what our N is. 0.35, that's our pi. And we need 14, at least 14. So it means we go to 14. Very, very difficult to work with this. Am I still on the right line? Yes. You just add those three. Which is 0.0015. 0.0015, which means it's correct. Exactly 14. So exactly 14 you just use. Exactly 14, which is that value there. 0.0012, which means that is correct. The probability that all 20 branches operated. All 20 means all of them. All 20 of them operated. Which is equals to... Isn't it 1? It should be equals to 1 if all of them have operated. Did I close it? What happened now? It opened twice. Okay, so we'll toggle between the two documents now. So this is the incorrect one. It should be equals to 1. Because it's all of them. So the incorrect answer here is C. I don't have to go through all of them. Because now this one where it says most 14. Then it means you need to... From here, you need to add all of these values. Starting from there. Starting from 0.12. Or you can say 1 minus 0.03. Because that's... So you can also just say 1 minus 0.0003. It should give you the same answer. Which will be 0.09. None of the 20 branches. So none of them, which means 0. So you just go to 0. None of them is 0. Which is 0.02. And that's what you will get. Can we do one where they ask the average number of branches closed during LL5 is 19? There? When they ask for the average number of branches closed during... So when they talk about average, then they're asking you to calculate the expected value, which is the mean. So you will say N times pi. I guess probably they should be some way where we will calculate that. So let's see. Yeah. For example, it might be a question like this. Average. So you just need to remember to use the mean. But now this one is not the one that I'm looking for. This one is Poisson, sorry. This is Poisson. If we are on this one, so the average or the expected mean they will be 20 times 0.35. And they can also ask you to calculate the variance of this. So your variance, which is sigma squared will be N times pi times 1 minus N times pi times 1 minus pi. And if they ask you for the standard deviation, you just take the square root of your variance. So if they ask you for the average or the mean, you can also call this the mean, the average or the mean. And if they ask you to calculate the variance, maybe I should also write by no meow at the top. And this is your standard deviation. Okay. So the next question is on Poisson. And how do I know that it's Poisson? Statements also do assist because in they, when you read your whole sentence, you will realize that they have given you all the information that you need. Okay. So a food traffic on the number of customers entering the mall was estimated to be 20 per minute. So on average, it's 20 per minute. Assuming a food traffic is Poisson distributed, which one of the following statement is incorrect. So now with Poisson, your table is divided by the lambdas. So it means they should have given you the lambda, which we can safely say here our lambda is 20. Let's go to the C. Yes. I used the study guide. It's there on the study guide on page 96. You used it there? The study guide. Lambda for 20. I'm saying the lambda for 20, it's on page 96 of the study guide. The study guide. Yes. What does it say? I mean, the table is there on page 96. Oh, you mean the table? Okay. So what's confusing me here is that 20 is not it cannot be a lambda. It cannot be an average. So if that is an average, then it means we're going to have to calculate this manually then because this is your, if you look on your table, does your table go beyond four on your study guide? It's up to 20. It has 20. It has 20. It has 20. Okay. So then we're going to rely on you to give us that. Let me see if I do have a study guide. Maybe I can open the study guide. Just give me. And you said it's page. This one might be old. It's page 96. Just before chapter six. It's page 96. 96. Okay. Page 96. So it has, so you can make note for yourself when you go answer questions on Poisson and they is our lambda of 20. So we do have that on the study guide. Okay. So we should be able to answer this question. So going to our question, our lambda is 20. And yeah, it says, what is the probability that 19 customers will enter the mall. So this is the probability of exactly probability of X is equals to 19, which is exactly. So you just go. 19. I think this. Which is that one that will give you your answer that you are looking for. That is correct. for the incorrect one. We are always not in class, but talking to somebody, please mute yourself. The probability that 35 customer will enter, so you just need to go to 35. If you can't see your table screen. You can see my table. What happened? Oh, yeah, right. Leslie. Yeah, I just want to ask you a question. Are you African or English? I'm I'm Twana. I'm not English or any. Yes, I am Twana. Oh, OK. It sounds like you're African. Yo. Yeah. Ah, ah, yeah. Yeah. Exactly because of the swearing. Oh, yeah, but can you speak Afrikaans or not? Maybe maybe me being in Cape Town for very long time had an influence. It's very funny. OK, so I think we are back now. Everything should be visible. So let's go there. Sorry, sorry, sorry about that. Oh, gosh, 90. There we go. I think we are there. So you go at this at 20. So the first one that we looked at was 90. So the next one, it says 35 customers. So we're going to look for 35. And there are your 35 customers. And then the next question says the variance. Now with Poisson, remember. You have your expected value, which is your average, which is also your variance. So what is the variance? That will be correct. Then the next one says at most 35. So yeah, we need to calculate the probability that X is less than or equals to 35. So now you need to do some work. You can either choose to add all these values from 0.7, 0.120, all of them, all of them, all of them. Or you can say in order for you to find the probability of less than or equals to 35, you can say it's the same as 1 minus the probability of X greater than 85, which then it means it will be 1 minus adding up all these probabilities, 0,004 plus 0,002 plus 0,001 plus 0,001. And that will give you the probability of less than 35. Do you have an answer? 0.992. 0.9992. And this one says the value is 0.15. So that is the incorrect one. And what is the mean? Maybe I'm going to make it clear. Change. And the meaning is 20. OK, that is poison. I see that our time is almost done. We are on part 12. Unfortunately, I have to go fetch my son at school at 4 o'clock. So that is why I schedule this from 2 till 4. In fact, there is nothing wrong with you continuing to do the discussion. Sometimes someone will have to share this screen or you can work through it on your own without anyone sharing. Or you can wait for me to come back at 5 o'clock and then we continue. We shall wait. OK, so we can take a break. Shall we wait? Yeah. OK. So do we exit and then come back or we will just wait just like this? No, let's save data. Let's exit and come back after 5 o'clock. I will let you know when I'm back in the house. OK. Thank you so much. I wonder if we're going to finish the exam tomorrow. You will see. Remember there won't be this explanation. You are there and doing the work. Yes. I just have a suggestion. Can you send us the PDF? Then we work on it whilst you're still fetching your kit. I will send it. I will send it. I will send the same one that we have here. Let me save it. So this one is not the online one. That's the same one. It's the same one. It's the online one. So now you will have the PDF. All right. So when you come back. Send it. I'm going to send it on the watch. OK, so because I think we also have people who are. From other groups. Yeah, who are not from the group. My group. So I will. You guys, you will sort yourself out. I will attach it here on the chat as well. And then some of you can. You will sort yourself out. Ask each other. How do I get that? Please send it to Jim. Please send it to Jim. To who? To Jim. And then he's going to post it on our group. OK, I think he also has a copy. But I will ask him if he doesn't. Then I will share with him. All the two types. Who are the other two types that I have? How can I forget my colleagues? Those are my colleagues. Let's do this. Wait. Just want to stop the recording. The recording will also be available on. Thank you.