Suppose that the time between successive occurrences of an event follows an exponential distribution with a mean of 1/λ minutes. Assume that an event occurs.
a. Show that the probability that more than 3 minutes elapses before the occurrence of the next event is e –3λ.
b. Show that the probability that more than 6 minutes elapses before the occurrence of the next event is e -6λ.
c. Using the results of parts (a) and (b), show that if 3 minutes have already elapsed, the probability that a further 3 minutes will elapse before the next occurrence is e -3λ. Explain your answer in words.