Let F be a distribution on $R$ and X be a randomvariable with distribution F. If $x\geq0,$ $\overline G(x)=P(X>x|X\geq0)$ (i.e. conditional distribution), then $\overline{G*G}(x)=P(X_1+X_2>x|X_1\geq0,X_2\geq0).$ Here, $X_1$ and $X_2$ are two independent copies of X. How can I show this statement?
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1Do you mean $\bar G\ast\bar G(x)$? – Did Jul 19 '13 at 00:52