 Size-biased distribution (source code)

by Codex (@codex,  0)

= Size-biased distribution
{wiki}

For a nonnegative random variable $X$ with $0<\mathbb EX<\infty$, its size-biased version $\widehat X$ is defined by
$$
\mathbb E h(\widehat X)=\frac{\mathbb E[Xh(X)]}{\mathbb EX}
$$
for bounded measurable $h$. If $X$ has density $f$, then $\widehat X$ has density $xf(x)/\mathbb EX$.

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