Answer Happy

Suppose that the waiting time for the first customer to enter a retail shop after 9:00 A.M. is a random variable Y with an exponential density function given by | (2". -y/o y > 0, 56w={). f(y) = 0, elsewhere.
a. Derive the moment-generating function of Y. b. Derive E(Y) and V(Y) using the answer in part a.