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Math Help - Poisson process & renewal processes

  1. #1
    Member Last_Singularity's Avatar
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    Poisson process & renewal processes

    Question: "Traffic on Snyder Hill Road is a Poisson process with rate 1 car per minute. That is, the times between cars are independent exponentials t_1, t_2, . . . with mean 1. Let T_k = t_i + ... + t_k be the time the k-th car passes. A turtle needs two minutes to cross the road. Let N = min\{i : t_i > 2\}

    (a) Find the expected value of T_{N-1}, which is the time until turtle starts to cross, and the expected value of T_N, the time the next car passes

    (b) Consider a renewal reward process with r_i = 1 if t_i > 2 and r_i = 0 otherwise. At what rate are rewards earned?"

    Thanks a bunch - I really appreciate it!
    Last edited by Last_Singularity; May 14th 2009 at 07:20 PM.
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  2. #2
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    Just to get you started, what is the distribution of N? Then use total expectation: E[T] = E[E[T|N]]
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