And remember the notes that we're using today are already shared with you on my entire screen. And yeah, so welcome to your first session of your exam prep, even though we have been doing this for the past six sessions. So this will be our seventh session that we are looking at different questions. Okay, so question number one. Which one of the following statement is correct with regards to variables and statistical inference? A. Quantitative variables are also referred to as categorical variables. D. Quantitative variables uses labels or names to describe attributes of elements. C. Qualitative variables have either an internal or interval or ratio scale of measurement. D. Conference is the process of using data from a sample to make estimate and test hypothesis about the characteristics of a population. That is, drawing conclusions, a population based on the sample results. E. Measuring attributes of an element result in a quantitative discrete variable. Which one of these five statements is correct? D. I would say D. D. Are we unhappy with D? Yes. D is correct because statistical inference. Statistics, we have two of them. We have descriptive statistic and we have statistical inference. Whereas descriptive just describe summarize the data into tables and charts. Whereas with statistical inference, we draw conclusion or we make inferences. And otherwise, the rest of the other statements are incorrect. Question two, considering the following information about type of variables related to auto, NOMAS vehicle, which one of the following statements is incorrect? A. Type or name of center used the car. Type or name of center used the car. E.G., for example, cameras, leader, radar is a quality. You just need to check the types of variable. The key words are type is type a qualitative nominal. The driving speed in kilometers per hour of an autonomous car is a quantitative continuous variable. The driving speed, is it quantitative continuous? Ask yourself. Question, do we measure it or do we count it? The size of a business in the self-driving car market that is small business, medium business, large business is qualitative ordinal. Ask yourself in terms of the size, which is described as small, medium and large. Is it qualitative ordinal? Is there an order or rank to that? D. The level of autonomy of self-driving car from low autonomy, moderate autonomy and high autonomy is a qualitative ordinal, same. The level, which is based on low, moderate and high, does it have an order or rank? The distance between the car and the front object is a quantitative discrete variable. Distance, is it measured or counted? E is incorrect. It is D. Which one of the following statements is incorrect? I think it's D. D. Okay, I hear D. What else? Anyone? E. I hear E. I hear D. I hear D. D. Because distance is measured. Sorry, I can't hear. Okay. We are looking for an incorrect, you must also bear in mind the following. In your statement, in the question, which one of the following statement is incorrect? Which one is not correct? It's incorrect. So those who say D. The level of autonomy from low, moderate and high, is there an order? Low, moderate and high. It's like saying small, medium and high. That is that. Is there an order? Yes, there is. If there is an order, then what is this level of autonomy? What type of a variable it is? It will be A. Qualitative, ordinal. If there was no order, then it would be qualitative. So. Order. You told me that there is an order. So it is ordinal. Therefore, it means the statement is correct. It's not what we are looking for. Or as with the type of name of sensor, it's qualitative because there is no order in terms of a camera or a radar or a leader. That will be correct. Let's look at E. E says the distance in meters between a car and the front object is a quantitative discrete. Now ask yourself, distance. Can you count distance or do you measure a distance? Measure. You measure the distance. And if you are measuring something, then the type of variable will be? Continuous. A quantitative continuous. And this one says it is a discrete. So that is incorrect. So the incorrect statement is E. So that's how you will answer the questions, even in the exam. Look at the key way and then look at what they are saying it is and confirm whether it's true or false. Happiness. Good. Thank you. Happy. Question three. In 2020, there was an estimated 3100 autonomous vehicle on the road in the world. The incomplete frequency distribution below shows the application or use of autonomous vehicle around the world. Complete the frequency distribution and choose which one of the following statement is incorrect. So let's first contingency or the frequency distribution. Where there is a question mark is for robot taxi. What is the amount? How do we get there? Actually, just tell me how will you get the question mark? The frequency. You minus everything from the total 3100. Thank you. Then minus everything from the 3100 and tell me what is left. 961. And 50. 61. 961. 961. Yes. 961. Okay. Now let's go and answer the question and find out which of the statement is incorrect. Correct. The percentage frequency, so we'll have to validate each one as we go along. The percentage frequency of a self-driving bus is 9%. How do we validate that? How do we find the percentage frequency? Divided by the total times 100. Yes. So we take the self-driving total, which is 279. You will divide that by 3100. And you will multiply the answer by 100% or 100. And that will give you the answer that we are looking for. Is that correct? Yes, it's correct. This one is correct. How do we find the relative frequency of civil autonomous vehicle? A frequency percentage or a percentage frequency is your relative frequency multiplied by 100. So how do we find the relative frequency of civil autonomous vehicle? It will be civil divided by the total. So it will be 31 divided by 3100. Yes. Do you get what is the answer? 0.01, which means B is the incorrect one. In the exam, you move on to the next question. You forget about the rest of them. Unless if you calculated incorrectly, then it's your own fault. But as soon as you get the answer in the exam, move on to the next one. Anyway, let's go on for this one because it's calculation. I want to make sure that you understand the logic as well. The relative frequency of civil autonomous vehicle for hay. You will take 800 and 68 and divide that by 3100. And that will give you 0.28. If they ask you, what is the frequency of robo taxi autonomous? You just go to the frequency table and get the answer. We did calculate that and 61. So that will be the correct one. The percentage frequency of self-driving. You will do the same as we did with the first one. Self-driving trucks are 527 divided by 3100 multiplied by 100. Easy there. Easy. Easy as lemon squeezy. Okay, moving on to the data below shows the production cost in thousand of dollars of 10 autonomous vehicle at Tesla incorporation. Calculate the interquartile range for the cost of production and choose the correct answer from the list above. What is the first step that you need to do is to check whether your data is sorted. That's the first step. Look at the information. If it's not sorted, you need to sort your data. First, we're talking about interquartile range. We can write this range IQR. You will go to your summary notes. You look at interquartile range there and you will find that it is 3 minus 1. Therefore, it means we need to go find the value for 3 and 1. And to find the value, you say 1. It's given by, you will find it on position and plus 1 divided by 4. Or you will find it on position 25%. Let's call it 0.25. You will use position 0.25 times n plus 1. That will give you split back value 1. And for quartile 3, you'll find it on 3 times n plus 1 divided by 4. Or you will find it on quartile 3 position on 0.75 times n. So you find the position. And once you have the position, you apply the rule. If you find it on 0.25, you round down. If you find it on 0.75, you round up. If you find it on 0.5, you take the average of the two values. So what is your quartile 1 position? So you will say there are 10 of them. So it will be 10 plus 1 divided by 4. And that will be 11 divided by 4. It's 11 divided by 4. 2.75. 2.75. Therefore, we go into estimate that it is on position 3. So you go to 1, 2, 3. That is your quartile 1. The same thing you can do it with this. It will be 0.25 times 11 plus 1. It will also give you 2.75. Which we can estimate that it is position 3. Do the same with quartile 3. What is quartile 3 position? Daily 3 divided by 4. 8.25. 8.25. 8.25. So it means also 0.25. And we can estimate that it is on position 8. 1, 2, 3, 4, 5, 6, 7, 8. So you just go and substitute into the values 2, 2, 8, 6. Minus 1, 2, 6, 3. And what is the answer? 1, 0, 2, 3. Which is option E? Option E. Happiness. Are we good? Yes. Question 5. Do you consider the production cost of 10 autonomous vehicle at Tesla? Provided in the table below. Now, which one of the following statement about measures of central tendency is incorrect? The first one says the distribution of the cost of production of autonomous vehicle is positively skewed. Therefore, it means what they are saying here. The mean is greater than the median. Always remember that when the mean is less than the median, it's negatively skewed or it's skewed to the left. If the mean equals to the median, it is the mean greater than the median. When we say it is positively skewed or skewed to the right. This one, it means the tail is to the left, and this one says the tail is to the right. This one is tail is to the left. And symmetric, it means they both equal size distribution. Okay, so that is the first one. You need to think if you answer that question. So it means you need to calculate the mean and the median. You need to find which is the most frequent, which is appearing. You need to find the median, and then you need to calculate the mode.  Remember, the mean is the sum of all values divided by n. Find the median by using the position and then go find the value. And then the mode is the most appearing or the most frequent. I'll give you five minutes to think about it. You don't have to say your answers. You need to calculate. I'll be back. Are we ready? Okay, so let's start with the mode. What is the mode? The mode is correct. The mode is the number that appears more than the others, which then the mode is correct. The median, how many are they? They were 10, so it will be 10 plus 1 divided by 2, which is 11 divided by 2. This is on position. 5.5. So it's located between two values. One, two, three, four, five. Take the average of the two values. What is the answer? 1519.5. Which is? Incorrect. Bale, mind that one. Did you calculate what the mean is? If you add all of them, divide by how many they are. The mean is correct. The mean is correct. And if I look at the first one, it says if the mean is greater than the median, then it's positively skewed. My mean is greater than my median. So A is also correct. The only statement that is incorrect is the mean. In the exam, do it the same way as I've done it right now, right? Calculate things that you are able to get immediately so that then you can get them out of the way. And the rest which are left would mean that if you haven't found your incorrect statement as you are doing the calculation, then the incorrect will be one of those that are meaning that if you have found your incorrect statement, therefore it means the rest of them are correct. You move on, but make sure that you did your calculations correctly as well. So we move on because our incorrect statement is C. On to question six. Question six. Now consider the production of 10 autonomous vehicles from Google, Waymo, Waymo from the table provided below. Calculate the standard deviation. You have two choices. Then you're running out. You're looking at your time. Use the things that you have at your disposal. Your calculator, your template. If you want to use Excel templates to calculate, use that. Use your calculator. Otherwise, if you don't know how to, this is the sample because it's not everything. So we're going to use s is equals to the square root of the sum of your observation minus square, everything divided by n minus one. That is the formula. Otherwise, you must go and use your calculator, put it in state mode, store the values and do the calculation. Excel, because this is something that we've never discussed even before as well, but done it in some of the videos previously. You need your Excel to have. Let me put it on bigger screen. When you go to data, it needs to have this data analysis. If you want, if you don't have that, it's fine. You can use the functions and I'm going to show you also now, but those who know how to use your calculators, go ahead and use your calculators. At first, I need to store the data. I'm just going to call this X. Doesn't matter. That will be my heading and I'm just going to put in my data. Six, eight, nine, and I'm going to put it in a column. Seven, five, seven, nine, one, three, nine, three, two, one, oh, nine, three, one, oh, nine, three, one, two, two, six, one, three, three, eight, one, four, one, five, one, four, seven, four. So I have all my data that is captured there. Then I'll go to my data analysis and I'll go to descriptive statistic. Okay. And I must input my data. I'm going to use X and I'm going to say it is my data is in a column because I've used the column. If I have put that in a row, like if it was in row two, I will select the row one. And I will also say there is the label in my first column or my first row because X is my label and I want to output the data on the same screen. So I'll just click on output range and click in the white area and click on column D. So D2 and I'm going to just only look at the summary statistic and apply it. Okay. And it would have calculated all the other descriptive statistics but we're not looking for all of them. You can use it with the previous question where they asked you about the mean, the median and the mode. You can do that with this one. So you can see that the mean, the median and the mode of this dataset are the same but what we are interested in is the standard deviation and my standard deviation is that one way of answering the question. The other way of answering this I can press equal and go to the formula and I go to more functions and you click on category I'll go to statistics and here are all the formulas and it says I'm looking for the standard deviation. It will say S P Q R S P and I'm looking for the standard deviation and you can also look at different ones. So this one says for the sample and also this one is for the population. You will see that it says the entire population and this says it is based on the sample. You can either use this one where it says the A or you can use this one. Sometimes they don't work but let's try with the S and I'm just going to include only those values and press OK and there is your answer. If you don't want to use the one that says ST or whatever the search you can use that you can use that or you can use I'm going to do the same with equal and then go to function again you can click on more function there or you can use the function more function I'm just complicating your life three days before your exam but these are some of the things you can use to practice also I'm going to only select the values I need and press OK and you can see that this that function they all give you the same the same answer sorry my bad things you can see they're all giving you the same answer whether using the data analysis panel or not if you are using a cache calculator I hope you do have that you need to capture your data I'm going to start by putting in the calculator to state mode mode 2 and we're looking for 1-va and we're going to put in the data 689 ENTA 757 ENTA 913 ENTA and I'm going to show you also on my calculator on the phone based on the link that I shared with you 932 ENTA and 1093 ENTA and 1093 ENTA 1226 ENTA show the site and 1338 ENTA 1415 ENTA 1447 ENTA and once I'm done I press the AC button and I'm ready, shift and you press the spat and we go to the var which is button number 4 and we are looking for the sx is the standard is the sample so we use the sx and xx is on button number 4 and you press equal and you will see that we still get the same answer which is option C so now let's do this that is if it will work if my I need to connect quickly just stay with me I must find the link and connect and hope that I will be able to ok it's refusing to connect me because it wants me to sign in and let's see because I did share with you the cup later on your phone but I've never really showed you how to use that and it's struggling to connect just give me a second if it's refusing then it's fine I'll see to tomorrow if I can sort it out and be ready with it tomorrow I don't know why I can connect to my phone ok let's just move on because I can connect it's refusing ok oh we know that the answer here is option C are we good unless if there is someone who is really struggling with how to use the version on your phone then we can do that tomorrow after I saw that my team is on my phone if there is no comment on that then we can sort it out later ok let's move on to question 7 which one of the following statement is incorrect with regards to experiment and counting rules and assigning probabilities A, an experiment with 3 steps and 2 outcomes possible for each step has 9 experimental outcomes B, the number of permutation of items that can be selected from a group of 7 item is 840 C, the number of combination of 4 items that can be selected from a group of 7 is 850 D, in an experiment with 5 equal likely outcomes each experimental outcome has a probability of 0.2 E, a statistical method of assigning probability is appropriate when experimental outcomes are equally likely this looks like an assignment question that we have been doing for almost every session that we do in the beginning when we deal with probabilities we deal with these questions the first one is multiplication rule N by N the B it's permutation N, P N, C, R P it's X over N and this is just the definition which one of these statements is incorrect I think it's number E, let's see number nope did you calculate A did you calculate B, C and D the answer is A, Lizzie the answer is A what is A? A would be 2 multiplied by 2 multiplied by 2 A A would be 3 steps with 2 outcomes will be 3 multiplied by 2 which is equals to 6 and the answer here says it's 9 and number B we have 7 and 4 always remember that the bigger number is your sample size so that will be 7 P P4 for option A wouldn't it be because it says 3 steps with 2 outcomes so you write step 1, step 2, step 3 and then the outcomes will be 2, 2, 2 where you multiply 2 by 2 which will give you 8 no, it's 3 steps and 3 outcomes and 2 outcomes for each step ah yes, for each step oh yes, you are right so it will be 2 times 2 times 2 times 2 times times 2 which will give you 8 here which is 2 times 2 is 4 4 times 2 is 8 which still makes incorrect option yes, you are right and for permutation that works out to 840 that will be 840 and for combination 85 it will be 7 C 4 which will be 35 and for the equally outcomes, experiments on dividing by 5 which will give you 0.2 it will be 1 divide by 5 which is 0.2 which is correct and the last one is your definition of what a classic method is and classic method is almost like defining how you find the probabilities it's a method of assigning probabilities and all experimental outcomes are equal like for example with number D or we did that which is correct moving on to question 8 the contingency table below shows the level of automation for autonomous vehicles and their users calculate the probability that an autonomous vehicle is used as a civil vehicle or that the level of autonomous is partial automation choose the correct option for the fact that they say or there what are we looking for we looking for the probability of civil or partial automation so I'm going to call this P and I'm going to call this C which is given by you need to know the formula remember in terms of basic probabilities the probability of A or B is given by the probability of A plus the probability of B minus the probability of A and B which is the probability of joint probabilities and if A and B are mutually exclusive if they are mutually exclusive then the probability of A or B will be the same as the probability of A plus the probability of B now when do things become mutually exclusive mutually exclusive events the probability of A and B will be equals to zero now if you know all these things let's look at this question they say we need to find the probability of civil or partial automation I've already defined them the COP if I look at the joint probability of C or B then the joint probability is equals to zero the joint probability will be equals to zero so it means they are mutually exclusive if there was an event there with a number they wouldn't be mutually exclusive so because of that joint probability of zero you can then write your equation as the probability of C plus the probability of P you could have just used this it will still be the same because this is zero so you can either use that or you can just say you will use the formula for mutually exclusive events how do we calculate the probability of C you take the total divided by the sample space which is 31 divided by 3100 plus the probability of partial which is 198 divided by 3100 remember that simple basic probabilities simple event outcome satisfying that simple event divided by the sample space and our sample space is 3100 and remember also that your symbol it's also marginal which means it's joint events the summation of your joint events and what is the answer 0.07 0.07 happy if you are lost speak now so it means you need to be able to know and pick up from the statements that you are given what is it the facts that are given to you and be able to identify which formula to use because if you read this sentence you need to know that you are looking at probabilities and you also need to understand which formula you need to be using are they asking you given or are they asking you about independence or are they asking you about joint events or simple events and yeah with the all I was able to identify that yeah we're talking about the addition rule because it's say either the statement let's say either one or the other if you can identify the next one once again consider the contingency table for the level of automation for autonomous vehicles and their uses calculate the probability that the level of autonomy for the autonomous vehicle is conditional automation given that the vehicle is used as a real pay choose the correct option from the list below what are the keywords from this given given you have given you have conditional and you also have grade how do you write that statement it will say the probability conditional maybe I should use CA and grade RH CA given RH now think about the basic probability somebody is talking or has something speaking in the background thank you think about the conditional probabilities so if I have given A and B and I say I need to find the probability that A is happening given that B already happened which is the conditional probability and we know that that is given by the joint event of A and B divided by the probability of a given event now think about that as your formula for conditional probabilities write the conditional probability for this and then I'm going to write it out for you and see if we will be right so the question says find the probability that conditional autonomy given that the vehicle is red given that the vehicle used is a red haig find the probability that A given that is B so let's see if we can write it in terms of in relation to the basic probability equation so it means we need to find the probability for joint event CA and RH over the probability of RH now think about it in this way because here they didn't give you the probabilities but they gave you event though you're still going to use observation satisfying the joint event divided by observation satisfying the simple event the same way find the probability so for the first one we need to go and find the probability of CA which is conditional automation and which is 179 so we're going to say 179 divided by 3100 divided by because it is the joint probability so the probability of A and B it's given by observation satisfying divided by N the probability of B it's given by observation satisfying the event divided by N we're going to apply the same concept for RH observation satisfying RH is a simple event so we're going to take 868 divided by 3100 CdS 179 divided by 8 68 there's 3000 in mathematical format that will be 3100 multiplied by we change the division to a multiplication and we flip 3100 divided by 868 which is that cancels out you are left with 179 divided by 8 68 what is the answer the answer is B the answer is 0,2 the answer is 0,2 that's correct that's how you will find the answer is that difficult not difficult but confusing not difficult yes it is so you need to always think about the original formula that you learned with the basic concept that we give you or that they give you in the study guide use that to apply to the question that you have that always works because then you do things in relation to the other so that you can understand step by step how to substitute the values into the formula and if they didn't give you the events they would have given you the probabilities you don't have to do the steps because with the probabilities you just substitute into the formula so if they would have given you already what the probability of A and B is here in terms of the values you just substitute that event or that probability into the formula and then do the calculation which saves lives instead of events events you need to first calculate the probabilities so that you can find the probability that you are looking for Moving on to question 10 the following discrete probability distribution shows the number of self-driving cars and the probability of spotting them in Michigan during traffic hours. Calculate the expected number of self-driving cars that can be spotted during the peak traffic. Choose the correct answer already they telling you that this is discrete probability distribution so this is your X and this is the probability corresponding to that so with that in mind to go to the discrete section of your study unit which is study unit 5 you go look for the formula to calculate the expected value which is the expected value is the sum of your X observation times its corresponding probabilities so it means you go into multiply your X and your PX and you're going to add them together that's one what they say so it's 0 times 0.52 plus 1 times 0.19 plus 2 times 0.17 plus 3 3 times 0.09 plus 4 times 0.03 or you can just go and say 0 times 0.50 1 times 0.019 is 0.19 and 2 times 0.34 is 0.17 is 0.34 and 3 times 3 times 0.09 it kills me it's 0.27 and 4 times 4 times 0.3 is 0.12 which is the same 0 019 0.34 0.27 0.12 and 0.12 and I might have gotten one wrong let's see 0.17 times times 2 and right what is the answer 0.92 the answer is D I think I think the last one is wrong the last one is yeah 4 times 0.03 is 4 times 0.03 is 0.12 just because that will be number 4 is correct yeah 0.12 that's what I also get so the answer is E double check so 0 times 0 052 will be 0 1 times 019 will be 019 2 times 0.17 7 times 7 is I must check that one so 0 so this one is the same as 0.7 which will be 0.34 this is 0.9 plus 0.9 plus 0.9 which 9 plus 9 plus 9 is 27 so 0.27 and 3 is 3 6 36912 0.12 so they are correct I didn't even have to use a calculator to calculate them because the values are so small are we good are we good or are we happy happy happy happiness if we are good question 11 question 11 states as follows consider a binomial experiment with prime trials and a probability of success of 0.9 use the binomial formula to determine the probability of exactly one success choose the correct answer from the list so it says we need to use the formula so the formula is NCR times maybe I should put the probability of X is NCR times the probability of so you will go to the binomial because they also tell you that so in the in study unit 5 you look for binomial you look at the formula that they use for the binomial you write it down 1 minus the probability of N minus X so since we know the formula let's go identify the things that we require to add into here so it says the number of trials which is your N the probability of success which is your pi and they say we must use the formula to find exactly one so it means our probability of X equals to 1 so it means where X we see X on the formula we need to put 1 so R I'm going to change R here to X because we use X so our N is 9 1 pi is 0.09 to the power of 1 times 1 minus 0.09 N minus X is 1 you need to do this step by step so that we are able to see what is it that we need to answer here right so let's go to the the next step is to calculate this so calculate NCR calculate 9 shift or second function and look for NCR and then press the 1 and then press equal so this is for the and this is for the so let's see what is the answer for N for 9 NCR 1 the answer here will be 9 combination 1 9 multiplied by 0.09 to the power of 1 is the same as 0.09 and the next one 1 minus 0.09 is 0. 91 to the power of 9 minus 1 is 8 now let's look at the options ok so looking at this option that cannot be almost it almost look like it ok so this one looks like it but it has some numbers so the next step let's calculate the ones without the powers together and see if it gets at some way so we can just ignore this one for now so 9 times 0.09 what do you get 0.81 0.81 and I'm going to leave the second part which is multiplied by 0.91 91 to the power of 8 let's see if we can find it on the answers correct one it is option C option C the moral of the story is I don't know try and work it out in many ways do different scenarios and I think because we've seen with some of the assignment they do like asking questions like this and so it means see if you are able to identify the formula you know how to work it out and not solve the whole thing because the challenge is because we all have case your calculators we might be quick to put in onto the calculator and try and answer the whole question at once based on the formula but that is not what they want you to do in terms of this they just want you to apply logic in terms of how you solve questions step by step so do that look at the options and look at what you need to be doing and let the option guide you in terms of the answers especially when it comes to this type of complex calculations happiness be good remember also this formula that I am using sometimes in state of using the NCX you can use the combination formula which will be your n factorial divided by your x factorial times n minus x factorial something like that moving on to question 12 which is second last question that we have recent reports of self-driving car crashes have resulted in safety concerns and consequently a delay in their rollout suppose the number of crashes is poison distributed with the mean rate of 0.1 crashes per year what is the probability of having one self-driving car crash in a given year so we need to look at poison go to the poison section of study unit 5 and for the formulas for poison or you are going to use the table because here they didn't say anything about formulas but we can use both so the first thing to do is if you are going to use the table let's identify what the mean rate is which is your lambda our lambda is 0.1 and we need to go to the question it says we need to find the probability of only one so x is equals to 1 car crash per year so we have a choice of either using the formula because it's easy e to the power of negative lambda lambda to the power of x divided by x factorial you can use this formula or you can use the table on the table you need to go find your lambda of 0.1 and you need to go find x of 1 on the poison on the poison table so it means on the table you will find your lambda there and you will find your x values there and where they meet that is your probability using the formula e to the power of negative 0.1 times I'm going to put it into bracket times 0.1 to the power of x is 1 divided by 1 factorial and I use my calculator and you can double check those who are going to the table remember to go into 4 poison table the poison table is broken down into different poisons so you're looking for 0.1 which is that value and we're looking for x so the answer is 0.0905 easy because it's only that the poison probability table 0.1 and the answer is 0.09 found that let's use the calculator on the calculator I'm going to take back two notes our e on your case or on your shop you will need to find find that I'm going to put the second function E 0 let me use my fraction fractions second I'll shift E the negative 0.1 use my arrow to come down multiply by 0.1 to the power of 1 is the same as 0.1 divide by 1 factorial will still stay 1 factorial where is my factorial and equal 0.0905 which is 4 8 which is 5 then the answer is option E same way as on the table I will find it as option E 0.0905 you can use the table or you can use the formula the only way to save time is to use the table imagine if they would have said at least then it means you'll have to add as many values if they say at most you would have to add 1 and 0 to get to the answer at most 1 you add 0 and 1 if you have to calculate using the formula so it means you'll have to calculate for x is equal to 0 and you have to calculate for x is equal to 1 and then add the values together using the table if you just go to the table you find the probabilities you add them together and that gives you your answer so it's easy to use the table time looking at our last question 20 minutes to spare let's see suppose Tesla conducted their own research and found the mean number of which is to be 0.1 4 car per year what is the variance of the number of self-driving cars so now that's the time you go to your notes and you look at it what is the mean what is the average is your expected mean or expected value which is also called the mean which is also called the variance so if they ask you a question like this what is your answer some of these things are like free free max that they give you you just need to know these things in order for you to get the question in search and that is how it's one way of answering some of the questions in the exam remember same time the minute you find the answer move on right move on to the next question we I'll say we started at half past three we took an hour to answer if I let's put it that way we took an hour to answer the questions because most of them I will say an hour even though we took one hour 10 minutes or 20 minutes to answer only session one questions if they are session one questions if you are alone then it means you can answer them in 30 minutes right you will because you don't have to do all the things that we have done looking at all the option of validating each and every statement taking long or asking and going there and there so you can answer your first session within 30 minutes remember if it's two hour exam make sure that you put an hour for session one and hour for session three and you pace yourself with you don't want to get to a point where the session ends your hour ends for your session one without you getting to question 30 you need to make sure that you get to question 30 to stand the chance because irregardless of how much you get in your session one well no, not irregardless remember this is supplementary whatever you get in your supplementary exam that will be the mark you will get at the end as your final mark so if your session one you get 100% of it session two you get 100% of it you will get 100% depending on how the calculations work right so pace yourself make sure that you complete both sessions session one is the easiest because it covers study unit one up until study unit five the majority of the things if you practice well and you know the formulas you should not go anywhere or anyhow wrong with answering the questions the only tricky part comes with study unit five and study unit four study unit four you need to make sure that you know the formulas and you know how to use the formulas to create new formulas based on the question asked like for example with these questions what is it that they have given you are they asking you to calculate the probability of all or are they asking you to calculate the probability of end you need to know how to define an independent statement because also probably in terms of the conditional probabilities as well need to know how to write a conditional statement based on the information given from the formulas that you know but if two events are independent what then does it say about conditional probabilities you need to know those things and it's easy to get it wrong because you always rely on what you know at that point but if you can master its section with what is required to answer this section what are the formulas that I need to keep in mind especially if you have the formulas with you because it's an open book for you to be able to know which formula to use take that summary note and use that as a guide because on there it gives you the formulas and it tells you which study unit is that and you should be able to use that to answer the question study unit 5 where it has three things discrete remember the table if they didn't give you the probability they would have given new outcomes you can calculate the probabilities but it's in the excerpt so they will not trigger that they will give you X and its corresponding probabilities not only that they can ask you to calculate the expected number remember they can also ask you to calculate the probability and based on at least at most equal exactly less than greater than you need to know how to get the probabilities based on that that is for the discrete probabilities as we can see that there is only one question in discrete then there is the binomia also with binomia they can ask you to calculate the probabilities or they can ask you to use the formula or they can ask you to find the expected mean the standard deviation or the variance of a binomia you need to know the formulas to calculate those with Poisson as well you can see that they ask you questions to calculate the probability or to calculate the mean the expected mean the variance or the standard deviation remember the standard deviation for a Poisson is the square root of your your standard deviation is the square root of your lambda that is for the Poisson once you have masters all this and you have all the formulas you should not go any hour wrong with answering the question remember not to panic don't allow the stress of not getting the first few questions wrong if you to get into your age if the first question you cannot answer do piggy piggy my Bellani and make sure that the next following question you get it you get it right and do not panic take your time don't panic don't rush but be mindful of the time so I don't know how else I can tell you how to prepare for this example other than that I'm going to stop recording and then we can have a discussion outside of recording unless if there is a question relating to the content