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Exponential Probabilities

  1. Sep 23, 2009 #1
    1. The problem statement, all variables and given/known data

    Let <d1,d2,d3...dN> be an odered set of samples from an exponential
    random variable with parameter lambda.
    Let <l1,l2,l3,...,lM> the same.

    Let Z = min<d1,d2,...,dN> --> Z is exp with parameter lambda*N
    Let U = min<l1,l2,...,lM> --> U is exp with parameter lambda*M

    2. Relevant equations

    Since we can write that:
    p(Z > U) = M/(N+M), which is in fact, p(d1 > l1)= p(Z > l1)

    How can I compute the following probability:

    p(Z > l2), p(Z > l3),...,p(Z > lN).

    3. The attempt at a solution

    Until now I am "approximating" this probability by assuming that:

    p(Z > l2) = (M-1)/((M-1)+N) and succesively, but I know it is wrong....

    Thanks a lot in advance!
  2. jcsd
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