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Math Help - HELP with Probability Result

  1. #1
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    Sep 2010
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    HELP with Probability Result

    Hi


    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):

    T=\min\left\{ T_{1},\ldots,T_{n}\right\}
    \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; September 1st 2010 at 05:19 PM.
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