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.
The base fee is 4 dollars, and the thing the at changes is x or the hours so the equation is 4 + 2x equals 12. and to solve for x we have to first subtract both sides by 4, getting 2x equals 8 then we divide both sides by 2 to get x equals 4 or 4 hours