exponential distribution help?

Question

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? (round to 3 significant digits.)

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? (round to 3 significant digits.

c)What is the expected time between your fifth and sixth messages?_______ hours

thank you!

Answer 1

If the inter-arrival times are exponentially distributed, the actual arrivals follow a Poisson distribution.

http://en.wikipedia.org/wiki/Exponential_distribution

Questions a and b are easily solved directly from the Poisson distribution:

http://en.wikipedia.org/wiki/Poisson_distribution

As for question c, think "independence"