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Math Help - independent exponential random variables having a common parameter

  1. #1
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    independent exponential random variables having a common parameter

    Let X1, X2, ...Xn be independent exponential random variables having a common parameter gamma. Determine the distribution of min(X1, X2, ...Xn)
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    Hello,

    Work with the cdfs... :

    Let x>0
    P(\min(X_1,\dots,X_n)\leq x)=1-P(\min(X_1,\dots,X_n)>x)

    But if the min is > x, this means that all the Xi's are > x.

    So P(\min(X_1,\dots,X_n)\leq x)=1-P(X_1>x,\dots,X_n>x)

    now use the independence to write it as a product of probabilities and finish it off
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