Let X be the time (in minutes) between two successive purchases at a commercial website. We believe that X has an exponential distribution with parameter alpha = 0.2 purchases per minute.
a. What is the probability that the time between two consecutive purchases at this website would be greater than 2 minutes?
b. What are the mean and variance of the time X between successive purchases?
c. What is the probability that there would be exactly 3 purchases at this website in a 10-minute interval?