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Multiple independent exponential random variables

  1. Nov 23, 2009 #1
    Let X1, X2, ....Xn be independent exponential variables having a common parameter gamma. Determine the distribution of min(X1,X2, ...Xn).




    3. The attempt at a solution
    I know how to do it with one X and one parameter but I am at a loss with these multiple ones....

    Thanks so much!
     
  2. jcsd
  3. Nov 23, 2009 #2
    Hint: min(X1,X2,...Xn)>x is equivalent to saying X1>x and X2>x and... Xn>x.

    You can find the latter probability by multiplying the probabilities of each event.
     
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