Question

At a certain time, the number of people that enter an elevator is a Poisson random variable with parameter λ. The weight of each person is independent of other person’s weight, and is uniformly distributed between 100 and 200 lbs. Let Xi be the fraction of 100 by which the i th 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.

Answer 1

Answer:

(a) MY(s) = e^λ(e^t-1/t - 1)

(b) E[Y] = λ/2

(c) E[Y] = λ/2

Step-by-step explanation:

See the attached file for explanation