= Mean residual life
{title2=$m_X(t)=\mathbb E[X-t\mid X>t]$}
For a nonnegative <random variable> with finite <expected value> and $\mathbb P(X>t)>0$, its mean residual life is the remaining conditional <expected value> after surviving past $t$. The <tail integral formula for moments> gives $m_X(t)=\int_t^\infty\mathbb P(X>x)\,dx/\mathbb P(X>t)$. The <exponential distribution> has constant mean residual life, equal to its original mean. In <excess of loss reinsurance>, the <total variance stationary condition for excess of loss> sets a candidate retention equal to this quantity.
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