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 = = 1, answer the following:

1. Show that the distribution of X is equivalent to an exponential distribution with mean parameter = 1. [Hint: remember that the pdf uniquely identifies a distribution]
2. Find the expectation and variance of the time between two successive arrivals.
3. Compute the probability P (X 4)
4. Compute the probability P (2 X 5)
5. Compute the 0.95th quantile of the distribution of X.