In questions. 78. We have information about a video rental store DVD rental store called Video to Go and were given a probability model in which we have X to be zero through five there, representing the number of DVD Reynolds per day for a customer and then the probability of each of those things happening. Now the four has 40.70 beside it, and looking at that, that exceeds 100% and that would not be a legitimate probability model. And then we would not be able to answer questions. Um, following this. So I think that's supposed to be a 1000.7 I think that maybe a textbook errors I'm gonna use this, um, as 0.7 for the rest of the problem. Also noticed that because they're probably model should add upto one. There's a gap without three. So we're mento. We're supposed to fund that gap. That gap is 30.12 and now each of those probabilities when you add them together, that adds up to one. Let's answer party A says. Describe the random variable x inwards. So X is gonna be the number of DVD Reynolds from video to go that is per day per customer be found The probability that a customer rents three DVDs? Well, that was the gap in the probability model. We've already figured that out. Um, that is 0.12 See, find the probability that a customer rents at least four DVDs, which that means four or five so or means ad. So four is point of 75.4 Those together may get 0.11 d. We want to find the probability that customer rents at most two DVDs, so at most two means zero or one or two. We can find each of those probabilities and the distribution above 0.3 plus 0.5 plus 0.24 That gives us 0.77 as our total. And then we're given information about a new store entertainment headquarters were given their probability distribution zero through five for DVD Reynolds and all of their probabilities. The probabilities do add upto one or 100%. Now, um, to make things simpler, I'm gonna change the X and the p of X and this one toe why? And people why, just when I calculate, um, there's a difference between video to Go and entertainment headquarters and E. It says, At which store is the expected number of DVD Reynolds Higher? Well, we're gonna find to the expected value of X, which is videos to go from the top and then the video of why, which is our new distribution. So in order to find your expected value, you're gonna take each value of X and multiply bites probability and add those together for video to go. We get 1.82 and we're gonna do that same thing for entertainment headquarters. Each value zero times it's probability, plus one times it's probability and so on, and we get 1.4 for its expected value. So the expected number is higher at the video to go in F. It says a video to go estimates that they will have 300 customers next week. How many DVDs do they expect your rent next week? So we would salute the expected value of 1.82 Well, that's the number of videos that we would x number of DVD rentals would expect per customer. If we expect to see 300 customers would just multiply those two values together and get 546. So video to go should expect 546 DVD. Reynolds Total and G says a video to Go expects 300 customers next week and entertainment headquarters projects that they will have 420 customers. For which store is the expected number of DVD Reynolds for next week. Higher. So we've already calculated, um, the expected number of DVD rentals for video to go in the previous question. Let's look at entertainment headquarters. We haven't expected value of 1.4 with a expected number of customers to be 420. We're gonna multiply these two values. Together, we'll get 588. Eso entertainment headquarters should expect Mawr DVD rentals next week. Um, 588 being greater than 546 and h which of the two video stores experiences Mawr variation in the number of DVD rentals per customer. How do you know that? So we can find the variation. We could find the standard deviation. Either one of these one. Answer the question. So I'm gonna look at the variation of X and the variation of why side note here is that variation is gonna be the summation of every single value minus the mean when I figure out how far away far away it is from the mean and square that value and then we're going to multiply it. By its probability, we're gonna add all of those together. So in X, as you can see, we have zero minus the mean, which is the expected number squared times. It's probability we're gonna then add that toe one minus the mean square times It's probability something with 2345 together. That adds up to be 1.3476 So the variation is 1.34 76 doing the same thing with why which is entertainment headquarters. We're gonna take zero minus. It's mean square that value to get rid of the negative, multiplied by the probability and do that with 1234 and five and do that all the way across. We get variation of to 0.4 so the various you can see is greater for why than it is for X, and we'll say that here, Entertainment headquarters says more variation and DVD Reynolds per week since the variation of why was greater than X 2.4 being greater than 1.3476 so why had a greater variance?