I have three questions about Poisson distribution and uniform distribution.

#89

I got the prob of success 6/25, but I cannot get the E(x) and Var(x).

#96

I am not sure how to calculate the sentence "Students make up 80% of those riding the elevator while faculty make up the other 20%."

#97

I got a and b, but I cannot get the correct answers of c and d.

The correct answers:

89. a. 12.5 b. 475/12

96. 0.049787

97. a. 11,000 b. 27,000,000 c. 5/18 d. 5/8

96. The number of people who ride an elevator in the Math Building is distributed as a Poisson distribution with an average of 60 people per hour. Students make up 80% of those riding the elevator while faculty make up the other 20% Calculate the probability that no faculty member rides the elevator during a 15 minute period. 97. Let the random variable L be uniformly distributed between 2000 and 20,000. a. Calculate the E[L] . b. Calculate the Var[L] . c. Calculate the probability that L will exceed 15,000. d. Calculate the probability that L will exceed 15,000 given that it exceeds 12,000. 92. You are given that X is distributed as a Poisson distribution with it =1 . a. Calculate the probability that X Z 2. b. Calculate that probability that X 2 2 given that X S 4