Title Paragraph Subtitle Subtle Em... Emphasis Int Styles 7 5. Let X and Y be independent; each is uniformly distributed on [0, 1]. Let Z = X + Y. Find: E[Z [ X]. Your answer should be a function of x. 0.2 if y = 1 6. Suppose that f(y | X = 2) = 0.3 if y = 2 0.5 if y = 3 Find E[Y | X =2]. 0 otherwise 7. Suppose that 250 students take a test, of which 100 are sophomores, 140 are juniors and 110 are seniors. Let X be the random variable representing the score of each student on the test. Suppose that the sophomores have an average of 60 juniors have an average of 67 and the seniors have an average of 77. Find E(X) using conditioning. Use the appropriate notation to explain your answer. 8. A business client of FedEx wants to deliver urgently a large freight from Denver to Salt Lake City. When asked about the weight of the cargo they could not supply the exact weight, however they have specified that there are total of 36 boxes. You are working as a Business Analyst for Fed Ex., and you have been challenged to tell the executives quickly whether or not they can do certain deliveries. Since, you have worked with them for so many years and have seen so many freights from them you can confidently say that the type of cargo they ship has a normal distribution with a mean of u= 72 lbs. and a standard deviation of o = 3 lbs. The plane you have can carry the max cargo weight up to 2500 lbs. Based on this information what is the probability that all of the cargo can be safely loaded onto the planes and transported? 9. Use Excel and the RANDBETWEEN(1,300) function to generate: a) 100 random numbers, b) 100 samples of size 5, and c) 100 samples of size 20. For each sample in parts (b) and (c), find the sample means. Create histograms for parts (a), (b) and (c). For part (a) use the random numbers (i.e. sample size 1), for parts (b) and (c) use the sample means to create the histograms. Copy and Paste just the histograms into your homework paper. Explain the differences in the histograms, You can do this using R if you prefer. ited States)