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Thread: HELP with Probability Result

  1. #1
    Sep 2010

    HELP with Probability Result


    During the course of some proof, I encountered the following given by the author and I cannot figure out how he came by this relation (the integral part):

    $\displaystyle T=\min\left\{ T_{1},\ldots,T_{n}\right\} $
    $\displaystyle \Pr\left(T_{1}=T\right)=\Pr\left(T_{1}=t,T=t\right )=\int_{0}^{\infty}\Pr\left(T_{2}>t,\ldots,T_{n}>t \right)\cdot\mathrm{d}\Pr\left(T_{1}=t\right)$

    I appreciate any help ...
    Thank You - Sam
    Last edited by mr fantastic; Sep 1st 2010 at 04:19 PM.
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