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Math Help - Exponential distribution.

  1. #1
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    Exponential distribution.

    a) Let X be the time until the next bus arrival. The time between two bus arrivals is
    exponential with mean 10 minutes. You come to the bus stop and see a friend waiting. You ask
    her how long she has been waiting, and she answers, 6 minutes. What is the expected time until
    the bus arrival?
    b) Now, suppose that bus arrivals happen deterministically every 10 minutes. How does your
    answer change?
    Last edited by mr fantastic; April 20th 2010 at 07:57 PM. Reason: Re-titled post.
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  2. #2
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    Quote Originally Posted by sadasoria View Post
    a) Let X be the time until the next bus arrival. The time between two bus arrivals is
    exponential with mean 10 minutes. You come to the bus stop and see a friend waiting. You ask
    her how long she has been waiting, and she answers, 6 minutes. What is the expected time until
    the bus arrival?
    b) Now, suppose that bus arrivals happen deterministically every 10 minutes. How does your
    answer change?
    I don't know the answer for (a) without doing research, but I believe (b) gives expected wait time of 2 minutes; the next bus arrival is between 0 and 4 minutes from now and the probability is uniformly distributed.
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