HELP with Probability Result

• September 1st 2010, 11:35 AM
siavashbabaei
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