Every student applicant at a certain university is declined with probability 0. In other words, each decision to admit can be modeled as a Bernoulli...

Q1: Every student applicant at a certain university is declined with probability 0.3. In other words, each decision to admit can be

modeled as a Bernoulli random variable. Assume that these decisions are independent. If the number of applicants in 2016 has the

Poisson distribution, with parameter 900, use the MGF to find the probability distribution of the number of admitted students. If the

probability that a student who starts his/her studies in 2016 manages to graduate is 0.9 (assume independence), what is the expected

number of students that graduate? 

Q2 At a certain time, the number of people that enter an elevator is a Poisson random variable with parameter l. The weight ofeach person is independent of other person’s weight, and is uniformly distributed between 100 and 200 lbs. Let Xi be the fraction of100 by which the ith person exceeds 100 lbs, e.g., if the 7th person weighs 175 lbs, then X7 = 0.75: Let Y be the sum of the Xi.(a) Find MY (s).(b) Use MY (s) to find E[Y].(c) Verify your answer to part (b) by using the law of iterated expectations.