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Math Help - Simple exponential function questions

  1. #1
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    Simple exponential function questions

    Given X_1,X_2,X_3 are independent and exponentially distributed random variables with respective rates \lambda_1,\lambda_2, \lambda_3.

    How can I derive P(X_1=min(X_1,X_2,X_3)).

    In fact I know the answer, it should be \frac{\lambda_1}{\lambda_1+\lambda_2 + \lambda_3}.

    Meanwhile I also know that P(X_1<X_2)=\frac{\lambda_1}{\lambda_1+\lambda_2}

    But I just can't seem to get it
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  2. #2
    MHF Contributor harish21's Avatar
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    Look at this link
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  3. #3
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    What about P(X_1<X_2<X_3) ?
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