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4 votes

Why does $E(V_n/(n+2)-1)^2=2/(n+2)$ when $V_n\sim\chi^2(n)$?

Let's expand the square and take the expectation of the expansion: $$\begin{eqnarray} \mathrm{E}\left[{V_n^2 \over (n+2)^2}-{2\over n+2}V_n+1 \right] &=& {\mathrm{E}V_n^2 \over (n+2)^2}-{2\...
jbowman's user avatar
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1 vote

Deriving the Reparameterization Trick

The reparameterization trick involves a change of variables to compute the expectation under the transformed density $p(\boldsymbol\epsilon)$. The expression $\int_{\boldsymbol\epsilon}f(g_{\theta}(\...
Gaurav Dhir's user avatar

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