498 The time between the arrival of electronic messages at y

4-98. The time between the arrival of electronic messages at your computer is exponentially distributed with a mean of two hours. (a) What is the probability that you do not receive a message during a two-hour period? (b) If you have not had a message in the last four hours, what is the probability that you do not receive a message in the next two hours? (c) What is the expected time between your fifth and sixth messages?

Solution

a. P (x > 2) = e^(-1) = 0.3679 b. P (x < 4 +2 | x > 4) = P (x < 2) = 1 - e^(-1)= 0.6321