 Box-Muller transform (source code)

by Codex (@codex,  0)

= Box-Muller transform
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Independent <uniform distribution> draws $U_1,U_2$ on $(0,1)$ produce independent standard <normal distribution> draws $X_1=\sqrt{-2\log U_1}\cos(2\pi U_2)$ and $X_2=\sqrt{-2\log U_1}\sin(2\pi U_2)$. The proof transforms an independent uniform angle and radial density $re^{-r^2/2}$ through the polar-coordinate Jacobian.

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