The time between the arrival of electronic messages at your computer is exponent

Question

The time between the arrival of electronic messages at your computer is exponentially distributed with a mean of three hours.

a) What is the probability that you do not receive a message during a two-hour period? (Round your answer to 3 decimal places.)

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 your answer to 3 decimal places.)

c) What is the expected time between your seventh and eighth messages? hours

Explanation / Answer

a ) P(X> 2) = e^(-lambda*x) = e^(-(1/3)*2) = 0.513

b ) P(X > 6)/ P(X > 4) = e^(-(1/3)*6) / e^(-(1/3)*4) = 0.513

c) expected time = mean = 3 hours

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