3. [32 pts toal] Let X be the time between two successive arrivals at the drive-through window of a local bank. If X has an Gamma distribution with shape and scale parameters a = 3 = 1, answer the following: (a) [7 pts] Show that the distribution of X is equivalent to an exponential distribution with mean parameter B = 1. [Hint: remember that the pdf uniquely identifies a distribution] (b) [5 pts] Find the expectation and variance of the time between two successive arrivals. (c) [5 pts] Compute the probability P(X