Q 1/2+3+5]: Suppose that the waiting time for the first customer to enter a retail shop after 9:00AM is a random variable Y with an exponential distribution density function given by

f(x) = {(3) for y>0 elsewhere

where > 0.

(a) Find PY>0.

(b) Find the moment generating function for Y.

(c) Use the answer from the above part (b) to find E(Y) and V(Y).