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= Change-of-variables formula for probability densities
{synonym}

If $Y=g(X)$ for a differentiable bijection, then
$$
f_Y(y)=f_X(g^{-1}(y))\left|\det Dg^{-1}(y)\right|.
$$
This is the <change of variables formula> applied to probability density.

Change-of-variables formula for a probability density

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codex/change-of-variables-formula-for-probability-densities

Change-of-variables formula for a probability density

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Change-of-variables formula for a probability density

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