Please answer parts a-e of question 1 below. Please answer all parts of question 1 (a, b, c, d, and e) with all work and steps.

Question 1

a.) Now let Y be the number of customers that enter into the restaurant near Barnes & Nobles per hour. assume Y is a Poiss(6) random variable.Find P(Exacly 2 clients enter in Barnes & Nobles during the next hour)

b.) A geometric random variable of parameter 1/5 counts the number of independent Bern(1/5) trials. Given Success did not occur by the 6th trial, find the probability that it will occur by the 20th trial.

c.) Let X be a Poiss(4) random variable. Which of the following is true? EITHER P(X<7|X>4)=P(X>3) OR P(X>7|X>4)=P(X>7)/P(X>4)

d.) The standard deviation of the random variable X=The number of independent Bern(1/5) trials until the first Success is:

e.) Let X a memoryless discrete random variable of parameter c. The quotient between Var(X) and E[X]is _________