 People still don't know what each assignment covers which study you need and people still don't know where to find the information and I thought before we start the session I just want to share with you where you can find all the other information in case people are also still not aware of where everything is at. I just want to change, switch the role to a student so that then you can see what you will be seeing. So this is the once you log in onto the system you will have multiple modules here as pay your registration modules that you have registered. If you register 10 modules and all 10 of them have E-tweeting and they also you will have your lecture site and then you will have your E-tweeter site. So your E-tweeter site will always have a number and an E at the end to show you that this is an E-tweeter site and your lecture site will just show the module number, the year and if it's semester it will have an S there and then that will be your lecture site. So to know what information is required for you to complete your assignment it is under the information it's here. If you go to announcement I think I am not sure. Announcements there is assignment availability and due dates. If you click on that there is a PDF document that you can download and you will it will tell you because all information is there. When is the assignment open and when it's going to be due? These dates are old, these are old dates you will have to check on the assignment thing. But what is important is what assignment number relates to what study unit. You can see that assignment two relates to study unit four and five. Assignment three which will be coming soon it will be open for July it will be study unit six and seven and so on. The dates will change and you will just I will just need to check with your lecturer again to update the document so that you can have the correct date. The other thing that you need to do is always check your your announcement. Don't ask other people don't rely on ESAs because the ESAs sometimes don't work well because we sometimes exaggerate when we explain things to people. So come to your lecture site and look at the announcement and look at the dates because the announcement updates them. So you can see there is the announcement on assignment two. It tells you what exactly is going to be happening. So you are aware of when the assignment will be open and when it's due. When is the closing date of that assignment because this was shared and you would have received this in an email as well. But not only this the material the prescribed book information everything is included here and you will be able to see your assessment or your assignment. Your assignments are called assessment. So you would have done your assignment one. There is the assignment two. It will only be open. For me I'm able to see this. I'm not sure if you are able to see it. But you can see there it's all the information. It's not yet available but there were some dates loaded on there. But don't worry about that. You had the announcement that explains everything. So you need to be able to come to this and look at everything that is happening with regards to your module. With regards to our eTutorials as myself as your eTutor we do have our own site. So you remember you will click on the one that says E1 which will be our site. What I want to alert you to is always the announcement you always get in your email as well depending on how you structured how you receive notifications. But the announcement I don't always post announcements here. It's easy for me to do it in the water but you can always come here. On some weeks I will also post some announcements here if I want everyone to be aware of what is happening if it's very very important. The additional resources are this summary note. You have all the notes from study unit one up until study unit 11 as per your content. This note relates to I'm going to show you now videos of content or related content. So you can use this study note to follow what is happening on those videos. I'm not going to touch the template the weekly session notes. These are the sessions that we have today. These are our weekly sessions. So those sessions today's session we do we dealing with Poison. They is the notes that we're going to be using for today. For your assignment two you will have to use study unit four session three session four study unit five session four and study unit five session five and study unit session six. Next week we will have another session which will be just the question and answer session of study unit four five and six combined oh sorry study unit five four and five combined. So I will find more questions that we can use to explain certain things as well for our question and answer session. But here is where you will find the notes. Okay so those are additional resources. Then there is this the folder called e tutorial and contents. If you click on it there are your study units. So it goes study unit one up until study unit five. So you will only be interested in those two study units. You just need to go through each one of them. Each study unit I'm going to go to the one that we are on which is this one. When you open you will get a coding which describes your discrete probabilities in detail and how you can calculate it and so forth and so forth. Then you just go to the next page you will get some quizzes where you are able to practice more and continue practicing. I think there are about three or four questions and then once you're done with the activities you can go to the next it will lead you to the next session which will be I'm not sure now where I'm at I clicked on the wrong thing. So once you once you are done it's once you're done with all the activities you will get to study unit five. Also you will find a recording that deals with binomial and poisson and then you just click on the next button and then you will do some activities relating to those two sections and then that will be it you will be done with with preparing for Sunday work. Then on Sunday we have the question and answer session where we do the activities like today we're going to get there. After Sunday you will go to the Sunday and get the recordings for all the online sessions they are under online. There you will be able to see all the weekly sessions that we had and you will just follow in terms of study units. So if you missed any of the session you can go to the date of that session and watch the recordings. So you just watch the recordings one after the other until you are done and then you start doing your assignment that's all what I wanted to get your attention to. If you want to know where to join the session you go to your calendar there are the sessions already preloaded onto the system you can just click on them there is the link to join or under the announcements under the announcements there is one way it might be you will have to you will have to go and find the correct announcement but it's one of those announcements where it's a weekly announcement probably it is this one. Online sessions I'm not sure if this has the link to attending the session but the links are always attached as you can see I always attach links to certain things on here so you should be able to find the link to attend the session as easy as like that. Okay so that's all what I wanted to share with you for for now before we start with this week's session so let's start with this week's session. So today we're going to be doing Poisson distribution likewise before I start are there any questions? Is there any question or clarity that you seek, iri that you have? If none can the person who hasn't muted themselves please mute yourself please stop music playing in your background. Always remember if there is music playing in your background please keep your mic muted because when we post the recordings if there is music playing in the background sometimes YouTube doesn't like it because of copyright we will have to cut it so imagine if we were doing some activities and your music is playing in the background it means the chunk of that activity will be cut off and you are disadvantageing other students from learning so please be mindful of that either ask the people to mute or to reduce the volume or just don't ask anything use the chat forum to communicate with us. Okay in the absence of any questions so we can start with the Poisson so by the end of the session today you should learn the properties of a Poisson probability distribution to be able to calculate the mean the variance and the standard deviation of a Poisson and you should be able to find the probability or calculate the probability of a Poisson distribution. Now like with the last time Poisson is part of a probability distribution and it is part of chapter five or study unit five it's part of the discrete probability distribution we have dealt with the properties we've dealt with the bilomial we are going to be doing the Poisson you don't have to worry about the other part of discrete probabilities not part of your syllabus and then going forward for your assignment three you will deal with continuous distribution okay so what is a Poisson distribution and what do we use it for so we use Poisson distribution when we are interested in the number of times an event is happening in a given area of an opportunity. How we define an area of an opportunity it is a continuous unit or an interval of time volume or such an area in which more than one occurrences of an event can occur and this can be the number of scratches in a car paint the number of mosquito bites on a person the number of computer crashes in a day. We apply Poisson distribution when you wish to count the number of times an event occurs in a given area of an opportunity the and we can calculate the probability that an event occurs in that one area of an opportunity and it will also fall in the same areas for all the other areas of an opportunities and you will see when we do some activities as well. The number of events that occurs in one area of an opportunity needs to be independent of the other number of events that occurs in the same other areas of opportunities because this is a random variable it needs to be independent for us to use it so one event cannot influence the other event or cannot affect the other event. The probability that two or more events occurs in the area of an opportunity approaches zero as the area of an opportunity becomes smaller and smaller then you will see when we go to the tables the Poisson distribution tables you will see that the probabilities of those events that are happening will become smaller as the the events increases as well. The average number of events per unit are always resemble or denoted by a lambda or that symbol that you see there that is a lambda that talks to the average or it talks to the expected number of events that we will use for the Poisson distribution. So some of the properties of a Poisson distribution is that we need to be able to calculate the mean we know that the mean is denoted by the lambda which is that lambda sign so from the beginning and this is the mean this is also called the expected value expected the expected value or the mean or the average or the average and the variance which is the sigma squared of our Poisson is also the same as your expected so we can also call this the variance because it's the same as your expected value the standard deviation however it is the square root of your variance so therefore the standard deviation will just be the square root of your expected value or your variance so with Poisson it is because you will be given the expected value so you you should be able to find what is there mean the the variance and you should be able to calculate the standard deviation of that expected number of events let's look at this example if this they tell us that a local police station receives an average 3.5 emergency calls per hour this calls follows a Poisson distribution and the question says find the mean of this question so we know the mean will be equals to 3.5 and the variance will be because the variance is the same as your expected number of event which will be equals to 3.5 because we know that our expected number of events is the same as your average is the same as your mean it's 3.5 the standard deviation which is the square root of 3.5 which will give us the answer of the square root of 3.5 is equals to 1.87 1.87 that's as easy as it is in order to work with the Poisson so if they ask you can play find the mean the variance they are all the same they are equal they are 3.5 and the standard deviation will be the square root of the variance which is the square root of 3.5 suppose that the number of daily fake news post is Poisson distributed with the mean of 0.2 this is your exercise what is the value of your mean and the standard deviation of the number of daily fake news post I'm going to give you one minute to think about this and one minute to answer this question we don't have to wait long if you know the answer already you can let us know what is the mean what is the standard deviation number one so they say it's number one so we know that the mean is the same as our lambda and our mean is the same as that this is our lambda therefore our mean is 0.2 and the next question they asked to calculate the standard deviation and our standard deviation sorry our standard deviation is the square root of our lambda which is the square root of 0.2 and the square root of 0.2 0.2 is equals to 0.45 I'm going to just leave it to 0.4 0.4 and that will be just number number one that was easy right calculating the probability we need to know how to calculate the probability using the formula and the formula is like that finding the probability of an x of an event where you are given the average of a number of events it's given by e which is the exponent the exponent which we also call it the base of the natural logarithm system don't use this number on your calculator you do have the e on your calculator it's e to the power of x on some calculators let me see on the casio on a casio it is the e is written in orange it will be that one way you will have to press the the shift first and then press the lean and that is the e that you will use to calculate the exponential e to the power of a negative lambda times lambda to the power of x divided by x factorial where x is number of events and lambda is your expected number of events how do we then calculate this you need whether we're going to use the table or not you need to be able to know how to calculate or at least substitute the values on today the formula and do some calculations so find the probability that x is equal to 2 given that your number of events or your mean or your expected value is 0.5 so we know our x is 2 our lambda is 0.5 we go to the formula and we substitute we substitute our lambda 0.5 we substitute our lambda 0.5 substitute x x is 2 so it will be e to the power negative 0.5 times 0.5 to the power of 2 divided by x factorial which is 2 factorial and when you calculate the entire value you get 0.0758 and that's when you are calculating manually same same same if you were asked to find the probability of a greater than you will have to calculate this same formula for multiple of those greater than values that you are calculating and then adding them all up we'll get to that exercises and we'll see how we apply that using a table so you do have a Poisson table and the Poisson table is divided by the lambdas as compared to the binomial table that is divided by the n values this one is divided by your lambdas your lambdas are always at the top of the table and each lambda values or each lambda values for each table corresponds with the number of x values and we look at the table just now the actual table so answering the same question that we have here we looked for the lambda table that has a 0.5 and we know that we're looking for x is equals to 2 we go to where x is 2 and where they both meet sorry where they both meet that will be the probability that we're looking for and you can see that whether you use the formula or use the table you will get the same answer let's look at the table the actual table so this is the table this table is 7 that you're going to be using to answer any of the questions that we're going to be doing just now so this table it's split up by the lambdas as you can see like as I explained the tables are broken down by the number of lambdas so this first one it's from lambda is 0.1 to lambda of 1 and you can see that it ends at 7 as it gets bigger and bigger and bigger the probabilities become zeros um if you add the sum of all this probability should also be equals to 1 so you should be able to calculate the probability of equal the probability of at least the probability of less than on this table now as you go with the lambdas you will see that the x values increases with the table as well you will see for the lambda 2.123 the table has 12 x values for 3.124 the table has 14 x values and like that it will go on on and on and on and on and on I'm not going to show you the entire table but at least you have an idea so this is very important because if they have given you and they say the average is equals to 0.9 and they say find that the probability of x is greater than is greater than four when they say it's greater than four therefore it means you need to add all these values of x then you will go to where it is 0.4 and 0.9 which is at this point you will have to add all these probabilities together and if they said it is the probability of x less than four then you will have to add all those other probabilities at the top similar if your lambda was 1.9 if your lambda was 1.9 then you will come to 1.9 and if they said it's less than or it's greater than four greater than four will be from here or sorry I did it all wrong because greater than four means you only add from from five you don't add four so you only add those ones so greater than greater than four does not include four so you exclude four so it means you're going to add all those values there so you just need to be very careful when you read your averages you need to go to the exact table that you are using okay remember always when we calculate the probabilities even for the poison we also are going to be given the weight problem sometimes we need to be able to convert the weight phrases into a mathematical symbol so that we can answer the question whether we want to calculate the greater than or equal or greater than or less than or equal or between and so forth and so forth so this is very important as well so let's look at an example a local police station receives on average 3.5 emergency calls per hour these calls are poison distributed what is the probability that the station will get six calls so because this is what is the probability that they will get it is exactly so therefore we need to find the probability that x is equals to six so we can use the function or the the formula which is the probability of e to the power of minus lambda times lambda to the power of x divided by x factorial which we then substitute then say e to the power of negative our lambda is 3.5 3.5 times our 3.5 lambda to the power of six because our x is six divided by six factorial and we can go to our calculator and start calculating okay our shift e minus 3.5 don't forget to put the 3.5 and I need to go down and by using my arrow multiply by and I can put the bracket actually instead of putting multiply by multiply by 3.5 close bracket then I do to the power of six and I'm gonna do equal because I didn't do the fraction button equal divide by and I'm gonna divide by my factorial which is six and the way is the factorial it sees on that shift factorial equals and the answer I get when I calculate is 0.0771 0.0771 now let's going to use the same and look at if we use the table so our lambda is 3.5 so I'm gonna go to the table 3.5 and that is our table I can make it bigger so that you are able to see 3.5 is our table and we're looking for x of six when they both meet and there is our probability so you can either use a table or use the formula to calculate okay what is the probability that the station will get at most what is at most what is at most uh at most means less there is the less than equal to at most certainly it's less than or equals to four calls therefore it means we need to find the probability that x is equals to zero plus the probability that x is equals to one plus the probability that x is equals to two plus the probability that x is equals to three plus the probability that x is equals to four so go ahead and use the formula it will take us forever so for quick use of the table will give us the answer quickly we still are on 3.5 so all we need is all the values from four and above and below it's all those values so we can write them because when I toggle between the two screens it will be distracting uh just write the values so you can give them to me when I go back to the slide let me know when we're done at least one person done you have all the values okay yes right so I'm gonna go back to the slide so with the probability of x is zero you can just give me the values it's zero point zero three oh two plus where x is one zero comma one zero five seven zero comma one zero five seven five seven four two zero comma one eight five zero four three zero comma two one five eight and four four zero comma one eight eight eight and then take your calculator and add all of them zero comma seven two double five zero comma double two seven two seven two seven two yes wait come again zero comma seven two double five double five and that is the probability that the station will get it most four calls per hour okay you get the you get it happiness we good all are we great good so far you have learned the properties of a poisson probability distribution you know now how to calculate the mean the variance and the standard deviation of a poisson distribution and you now also are able to know that you can calculate the probability of a poisson distribution by either using the formula or by using the table so now let's do some more exercises for practice how do I get rid of this thing there we go let's go the number of power outages at a nuclear power plant has a poisson distribution with a mean of outage of six outages per year so we know that is our average which one of the following statement is incorrect so you need to go to your table and answer the following questions so we can do it together this the first question we will do them together and then you will go and I will give you more time to do them on your own as we go along the probability that there will be no outages it means we need to be finding the probability that x is equals to zero right because zero will represent no outages in that hour so we go to six so you need to go to the table with the average six and they is our average of six average of six and x is zero and the probability is zero comma zero two five and they okay so on this table they used a table that has five decimals so it will still be zero comma two five and the table that I'm using is four decimals so it's rounded off and that's what you might also I get if you are using a prescribed test book sometime it might have five decimals if you are using the study guide it might have the same tables as I have if you're getting from another or internet or somewhere it might be four decimal or five decimal so you just need when you go write the exam they will give you the table oh they yeah probably they will give you the tables that you will use so you won't have this mismatch of information as well so that is the same so that is correct the probability that they will be at least what is at least at least one that will be the probability that x is greater than or equals to one that can also be one minus the probability that x is equals to zero or you can do you can say is the same as because it says at least one you will go and find the probability that x is equals to one plus the probability that x is equals to two plus the probability that x is equals to three plus all of them so let's go back to the table we're still using the same table because all the information is related to six so you'll come here and you will add all these values there instead of adding all the values we can just take the probability of a complement of all the values which is the probability of x is equals to zero which we know that now that it was one minus zero comma zero zero two five and that will be equals to that will be equals to one minus point zero zero two five is equals to zero comma nine nine seven which is the correct one that is the zero comma nine nine which means that is correct if you have any question or you don't understand what i'm doing yeah please stop me and ask why am i doing this or that so that we are able to clarify things but you do understand why i'm doing it this way right okay no i'm done the probability that there will be more than one outages what is that they are asking you to find the probability that x is greater than one so now this is different to the previous one because the previous one said it is at least so this one will be one minus the sum of the probabilities of x is equals to zero plus the probability that x is equals to one because it has to be for both of them because it says more than one so more than one means coming to more than one will mean all these other values except those two so in order for me to not add all these values because it's going to take me forever to add values from two up until 17 i'll rather add those two and subtract them from one because those will be the complement of all of them so that will be i'll just add those two 0.025 plus 0.0149 0.0025 minus 0.0149 i think i forgot to subtract them from one minus and the answer is do you have the answer 0.9826 0 that's after saying one minus answer yeah 0.98986 you let me hang in six sorry so therefore that would be the incorrect one but for the purpose of practicing we continue the standard deviation of the number of power outages is 2.45 so we know what the so we take the square root of six what is the square root of six 2.45 so that would be correct the number of power outages has the mean of three that is correct because we were given six for a year so semester we're just going to divide by two thank you because i didn't read the entire sentence and that is correct okay so those are how you're going to oh this is how you will answer the questions when get them from your assignment or the exam as well so you can be given questions to calculate the probability or calculate the standard deviation or the mean and so on let's look at the next one so this one also you can do it yourself suppose that the number of daily fake news is poison distributed with the mean but i think we did this oh sorry we did that we found that it was number two sorry i used it in the exercise we can skip number two because we did find this was the square root of zero comma two which is zero comma four the average number of adults with ASD consulting with a neuropsychologist per day is poison distributed with an average or the mean of 1.5 so that is your lambda what is the probability that on any given day a neuropsychologist will consult with only one adult now therefore you need to find the probability that x is equals to one you can either use the formula or use the table and because you will be using the process of elimination you will first go and find that on the table so let's go to the table 1.5 right to 1.5 1.5 this 1.5 and we want x is one so x is one and the answer is 0.3347 right the answer is 0.3347 none of them none of this none of this none of this so we are left with only two can we select number five i need more information to calculate the probability not necessarily because we do have all the other information and we did find the probability there so that won't work but we cannot assume that this is not the correct answer as well or this is the correct answer let's choose our formula so looking at this the way they have it i can just write the formula it's a good number four sorry ma'am yeah i'm sorry i calculated number four i got it it's correct yeah i'm just with number four so they yeah is the formula i introduced to you you can rewrite this formula as lambda x e to the power negative lambda over x factorial so let's substitute everything that we know into this formula to see if we can get the same answer as that so our lambda is 1.5 our x our x is one always in the question e to the power negative lambda of 1.5 divided by 1.3 so number four is our correct answer so you need to pay attention when you answer questions especially Poisson or binomial as well where they can give you the formula substituted formula or halfly calculated they would have calculated it halfway and they asked you to answer the questions so you just need to pay attention to that and this is one of those scenarios so they just wanted to see if you know how to substitute back into the formula based on the information given and okay to the next question suppose call center agents absences are Poisson distributed with the mean average or the average of three so our lambda per day using the formula to calculate the probability that five agents are absent on a randomly chosen day choose the correct answer from the list so they telling us that x is five so we need to find the probability that x is equals to five and we read from the it said use the formula so I'm just gonna write the formula I'm gonna write the formula you continue and do it lambda x I'm just gonna use this way because I can see that the answer is written in this manner Ryan answer that question if you have an answer just let us know which letter I think it's you think is I think it's it's e it's option e option e you think it's option e okay okay others do you agree I agree with her because I got the answer as 0.1008 you did you simplify the e you don't have to simplify the e yeah I don't think we have to simplify the e because it looks like they only said the lambda to exponent x divided by x factorial only so what is our lambda our lambda is three our x is five five you can use multiply as well since they are using multiplication everywhere multiply by e to the power of minus three divide by five factorial so what is three to the power of five two four three it's two four three that is two four three times e to the power of negative three what is five factorial it's 120 120 and we can 120 can go into 243 and it goes 2.025 multiply by e to the power of three which is option yeah so you need to be very careful when you answer the questions look at the options don't try and solve the entire question before looking at the options what is it that they have given you because sometimes they will give you an option here that says none of the above and I'm sure you're going to choose the none of the above but there is an answer as we can see there suppose we know that knowledge that the number of students absent at one of the st a 1610 session are poison distributed with the mean of 2.5 per day what is the probability that at least two students are absent on a random chosen day so that is we need to find the probability that x it's greater than or equals to two you can do this two ways the first way is to say the probability of x is equals to two plus the probability of x is equals to three plus up until you get two we are on 2.5 2.5 ends at 12 up until you get two plus the probability that x is equals to 12 or the shorter way probability of x is greater than or equals to two is the same as one minus the probability that x is less than two which is the same as one minus the probability that x is equals to zero that's the probability that x is equals to one which will be the shortest way let's go to the table so that those without the table can have the values are we using 2.5 and you will just choose the two values are we done I just question are we not going to include two you can include two because this set the probability that x is equals to or greater than two so it means this needs to go in this way we'll have to include two but going to the compliment the compliment cannot be true oh that's why I did like that I think option one a is equal to one zero comma seven one two seven all right so the probability that x is zero was zero comma zero eight two one plus zero comma two zero five two you just say one minus zero comma zero eight two one minus zero comma two zero five two let's see if your answer is right one minus you can put it into the bracket point zero eight two one plus point zero point two zero five two close bracket equals zero point seven one two seven as you said it which is option a so you can also check it if you are not sure you can check it by adding all these values so at least we will add up until 10 because 11 and 12 are zero zero should give you the same answer let x be a random variable representing the number of mistakes in a textbook suppose the mistakes okay add an average of two page two per page the probability that at most three mistakes are found on a given page is what our lambda is and we are asked to find the probability at most three will be x it's less than or equals to three which is the easy one x is equals to zero plus the probability that x is equals to one plus the probability that x is equals to two plus the probability that x is equals to three i'm gonna go to lambda of two i'm gonna give you a time to look at the table lambda of two is the top one let's remove the ink so the last question so this is zero one two three four the math it's zero one two and three just write all the values are we done yes what are the answers option one but i need the values sorry zero comma one three five three and the next one is zero comma two seven zero seven and i think the next one also is the same the same yes and the last one is zero comma one eight zero four okay and when we add all of them zero comma eight six zero comma it gives me zero comma eight six your calculator that is zero four decimals zero comma no it's supposed to be zero comma eight five seven zero comma eight five seven seven eight one does it end there yes oh because we're using a four decimal table probably they used in this tutorial letter they never used the four decimal values which is option number option one no i don't know why my calculator is just giving me the answers with two decimals what calculator are you using i'm using sharp financial calculator okay there we go press setup zero zero and then press four then your calculator will be on four decimals all the time okay you said set up and then i wrote it here set up and zero and then four then your calculator will be on four decimals if you want to take it to two decimals you just repeat the step set up oh yeah set up zero zero four set up zero zero two will take it to two decimals so that zero zero four will take it to four decimals so here we go so always when we do probabilities just keep your calculator on four decimals actually just keep your calculator on four decimals and round it off when you get to the answer okay let x be a random variable representing the number of mistakes in a textbook we have done something like this similar the average which is the lambda is two per page what is the probability that at least the probability of at least what is at least at least five what is at least five greater or equals two what is at least did we cover at least let's go back i think we did right did we cover at least we covered exactly not at least hey so we did cover at least yeah there is at least why am i okay it's sunday it's exactly not at least what am i talking about exactly that is exactly five what is exactly five equals to five yes it's equals to okay all right so what is our lambda is two x is five so let's go to the table it should be easy and quick to answer lambda is two x is five lambda is two x is five the answer is zero comma zero thirty six one it's option four because my values here are in five decimals four decimals that if you round it off it will be zero comma zero three six one which is the same as what we got from the table assume that x is a Poisson random variable with the average lambda of six which one of the following statement is incorrect so we need to evaluate each and every one of them what i will do go into you stop zinting and bring the table close back we know that we look you for six right so i can just go to a lambda is six will be at the end which is this one so i'm just gonna leave it next on top of the presentation so it means i would be able to write with me lambda of six i'm gonna write the numbers here one also zero you to be able to reference zero one two three seven eight ten eleven twelve eighteen fourteen fifteen sixteen seventeen okay so let's look at number one number one we're looking for the incorrect one so look at number one don't tell me the answer is yet we will do the answers once we are done with looking at the options we're evaluating all of them write the answer the correct answer for number one look at number two number two set the variance is 2.45 is that the variance remember is the square root of your lambda number three find the probability of x less than three write the the values down number four says find the probability that x is greater than five remember you can do it two ways instead of adding from six to seventeen you can add from five yeah you can add from five to one and subtract that from from one and then the last one they are asking me to find the probability of between which is number five and remember this is exclusive because it's just between two and five but that's not include two and five got it are we happy please start okay can i remove the table or you're still busy i'll leave the table there for some time for those who are still busy for each of reference i have just posted it there for us to use let's answer the question we're looking for the incorrect one right the probability that x is equals to zero we just go and find that probability it is zero comma zero zero two five so that is correct the variance remember is just the square root the variance will be the square root of six and i think we did calculate this area is that correct did we find it as two point four five right yes it's correct question yes no oh no the variance the variance supposed to be equal to yeah supposed to be the lambda i equals to lambda yes you are right because the standard division is the one square root yes so that would be the incorrect question the incorrect answer because they're asking for the variance the probability of less than three just for practice papers less than three therefore we need to add all these values excluding three we add all the other values so you will add zero point zero zero two five plus zero comma zero one four nine plus zero comma zero four four six add them all together they should give you zero comma six two one zero zero two five plus point zero one four nine plus point zero four four six equal that's the right answer the next one says the probability of x greater than five this we can find it by finding one minus because there is the probability of greater than five we can then find one minus the probability of x less than or equals to five because that will be the complement of five which is the same as one minus we already have the less than three which is those ones so we can just add minus those ones values which are zero comma zero six two which is all of those and then we just add the next ones plus zero comma one three one three zero comma zero comma zero eight nine two plus zero comma one three three nine plus zero comma one six zero six i'm just gonna add the rest of the other values absolutely am i losing you by doing it this way remember this zero comma is this values i'm not going to repeat them here because we already calculated them there i need to find that the probability of less than five less than or equals to five is zero one two three four five so it's all of this in our previous question we did less than three which means we added all those so the only thing i need to is to also include in the previous question that from the zero comma zero six two to add the others that are not there because i could replace this zero comma zero six two with all these values and then it would be a whole long number is that what you asked me here i'm also showing new shortcuts that you don't have to sweat a lot but we need to pay attention when you do that so here i have one minus zero comma four four five seven minus zero comma four four what did i get five seven right then i can subtract one minus point four four five seven and the answer is zero comma five four three she's the same this might be have which then this is correct the last one says we need to find the value of between two and five the values that are between two and five is the probability of x is equals to three plus the probability that x is equals to four which means we just add zero comma zero eight nine two plus zero comma one three three three three nine point zero eight nine two plus point one three three nine zero point two two three one which is correct any questions you need to practice it requires you to practice even with the shortcuts you need to practice this because then it can be confusing especially when it comes to the sides because if if the sign here it says greater than the complement of it will be one minus the less than or equal including that number if it was greater than or equal i was confused when you say zero comma when i wrote this on number four yeah on number four i was confused when you say zero comma zero six two so i didn't know where you got it oh sorry i thought i explained that because we already calculated it previously those three numbers and i said those three numbers are those three numbers we already calculated them and we found them it was zero comma zero six two i don't have to rewrite them i can just write the sum of them oh i got you i got you thank you that is the sum of those values because we needed to calculate from here to above otherwise you can also calculate all these values going there from six downloads so in order in state of 81 2 3 4 5 6 7 8 9 10 11 12 you can just add 1 2 3 4 5 6 6 and in state of 86 because you already added the three you just add three numbers four numbers together okay so we almost at the end of the session likewise i do have extra questions included in the notes that you can go through them on your own so here is the other question you will notice that most of the questions are almost similar the the the difference is we change like the question will change a student to john john to Mary to Paul Paul to a factory factory to something else but if you read carefully the question you will notice that the questions are almost exactly the same it's just that the the environment changes but your lambda will stay lambda your x will stay x your probability and answering the exactly or greater than will stay the same for all the questions so this is one other question that you can do on your own they gave you the lambda of 0.2 and you need to just evaluate each one of them to find the correct answer in here number one and number two they are equal number three and number four it's exact it's at least so it's greater than or equal question 10 using the same information from there you can see that you need to calculate the probability of any given day that there will be no fake news no means zero so you can find out whether it's any of this and if not then use the formula to check if this is the correct one remember you don't have to simplify the entire formula you just need to substitute and simplify the numbers except the e the natural log base okay and then but also you must pay attention because on the log base it is to the power of a negative number so there are certain things that you need to pay attention to when you look at the questions as well and remember you're looking for uh what is the question you're looking for the exact probability and other questions can come to you in this manner you just need to make sure that you understand that that is your mean average and that is your why and you calculate the same average calculate the variance uh yeah you need to calculate the probability of at least seven so it's greater than seven greater than one for two points five at least two and that concludes today's session so there are a couple of questions that you can still go ahead and practice with except the one including not except including the ones that are on the content and video activities as part of the e tutorial that you can use also to practice other than that by the end of this session today you have everything you need to be able to answer your assignment two with ease so it means if you haven't caught up with all the work you need to go back and revise your study unit for recordings for the content and also for the activities that we did on a Sunday you need to look at the three recordings that we have already on binomial uh discrete probabilities binomial and today's one on points one plus including also the content videos now if you haven't caught up it means the content videos are two hour session videos so it means it's four hours that you need to set aside the Saturday Sunday sessions they this are one hour 30 minutes so there are four videos that probably five let me assume that there are four videos so of the four videos that are there so it's one and a half one and a half makes three hours so it's six hours so you need to set aside 10 hours to look at the recordings thoroughly to revise in order for you to be able to go and do your assignment and i'm saying this pleading with you because without watching the recordings you might struggle to do some of the easy questions that are there or are asked so please make time before you even start your assignment to watch all the recordings you need 10 hours to catch up to everything that we have done and then start your submission one remember you will have another submission closer to the end of the closer to the due date of your assignment at least once you have done your first submission we have one last session where we will answer question and answer based on chapter four and chapter four we call it study unit study unit four and study unit five where you can ask any question you can ask ask to clarify certain things that you're still unfamiliar with to help you with how to read the table if you're still struggling with your table to help you with how to use your calculator to calculate either the binomial probability or to calculate the place on which will be the last session that we will have a week before the closing date of your assignment then the following week we're going to start with preparing for assignment three so there is no time to rest you just need to make sure that you catch up other than that if there are any questions feel free to ask if there are no questions enjoy the rest of your weekend thank you for showing up and thank you for being here thank you very much thank you thank you thank you thank you evening