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Math Help - Exponential Distribution problem

  1. #1
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    Exponential Distribution problem

    Hi Members,
    Problem is as follows.
    C arrives at a two-server post office to find A being served by server 1 and B by server 2. C will enter service as soon as either A or B departs. If the service time of server i are exponential random variables with rates $\mu_i=1,2 $, find
    a)The probability that A is the first one to depart.
    b)The probability that A is the last one to depart.
    c)The expected time until C departs.

    Solutions:
    I don't know what are the correct solutions, but I solved them as follows.
    a)$\frac{\mu_1}{\mu_1+\mu_2}$
    b)$\frac{(\mu_2)^2}{(\mu_1+\mu_2)^2}$
    c)$\frac{1}{\mu_1}\left( \frac{(\mu_1)^2}{(\mu_1+\mu_2)^2}\right) +\frac{1}{\mu_2}\left( \frac{(\mu_2)^2}{(\mu_1+\mu_2)^2}\right)$
    Please reply me, if my solutions are wrong.Your comments about the correctness of answers are always welcome
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  2. #2
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    Re: Exponential Distribution problem

    Hi members,
    Are these problems so difficult that no members know the correct answers?
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