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I am studying probability and finding hard to understand the following equation.

$Pr[P_i \leq \min\{P_s;s \neq i\}]=\int_0^\infty \underset{s\neq i}{\prod}[1-G_s(p)] \, dG_i(p)$

where $P_i$ are random variables, $G_i(p)$ is a cumulative distribution function $G_i(p)=Pr[P_i \leq p]$

Could you explain me how to get the right side of the equation? what theory dose it use? Thank you!

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  • $\begingroup$ IOt is impossible to understand your question until you define your terms! We are not mindreaders here. $\endgroup$
    – kjetil b halvorsen ♦
    Commented Nov 15, 2015 at 13:57
  • $\begingroup$ Please add the [self-study] tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. $\endgroup$
    – gung - Reinstate Monica
    Commented Nov 15, 2015 at 14:28
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    $\begingroup$ For any given $p$, ask yourself "what is the chance that $P_i$ is approximately equal to $p$ and all the other $P_s$ exceed $p$?" This will help you understand the right hand side. $\endgroup$
    – whuber ♦
    Commented Nov 15, 2015 at 14:31
  • $\begingroup$ I'm voting to close this question as off-topic because the OP has not responded to questions $\endgroup$
    – Peter Flom
    Commented Sep 14, 2018 at 10:56

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