Suppose that the amount of time between consecutive surges in an electricity network has an exponential distribution with rate of one surge every fifteen days.
(a) What is the probability that the next power surge happens at least 50 days from now?
(b) What is the probability that the next power surge takes place five to twenty days from now?
(c) What is the probability that exactly four power surges occur in the next thirty days?
(d) What is the probability that fewer than six power surges occur in the next sixty days?
(e) What is the probability that the next power surge will occur within the next seventy days, given knowledge that the next power surge will not occur within the next fifty days?