 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

For $w\geq0$, $\mathbb P(W\leq w)=\mathbb P(R\leq\sqrt w)=1-e^{-w/2}$. Differentiation gives
$$
\boxed{f_W(w)=\tfrac12e^{-w/2}\mathbf1_{\{w\geq0\}}.}
$$
This is an <exponential distribution> of rate $1/2$, with <mean> two and <variance> four.

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