Problem A: The time between the arrivals of electronic messages at your computer

Question

Problem A: The time between the arrivals of electronic messages at your computer, X, is exponentially distributed with a mean of two hours. ) 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? d) Find the quartiles of the distribution of X. e) Determine time c such that the probability that you wait for a message more than c minutes is 0.20. What is the name of c?

Explanation / Answer

a ) P(X> 2) = e^(-lambda*x) = e^(-(1/4)*2) = 0.606

b ) P(X > 6)/ P(X > 4) = e^(-(1/4)*6) / e^(-(1/4)*4) = 0.606

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