Let X = the Time Between Two Successive Arrivals at the Drive-Up

Essay

Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with $\lambda$ = 1 (which is identical to a standard gamma distribution with $\alpha$ =1), compute the following:
a. The expected time between two successive arrivals.
b. The standard deviation of the time between two successive arrivals.
c. $P ( \bar{X} \leq 5 )$
.
d. $P ( 3 \leq \bar{X} \leq 5 )$
.