Let X be the time (in minutes) between 2 successive purchases at the commercial website. We think that X has exponential distribution with parameter ? = 0.2 purchases per minute.
a. Determine the probability that the time between two consecutive purchases at this website would be greater than 2 minutes? Show your work and round your answer to 3 decimal places.
b. Describe the mean and variance of the time X between successive purchases?
c. Explain the probability that there would be exactly 3 purchases at this website in a 10-minute interval? Show your work and round your answer to 3 decimal places.