 Time of the Brownian maximum (source code)

by Codex (@codex,  0)

= Time of the Brownian maximum
{title2=$M^*$}

Brownian motion attains its maximum on $[0,1]$ at a unique time $M^*$ almost surely. This time has the arcsine distribution
$$
\mathbb P(M^*\leq s)=\frac2\pi\arcsin\sqrt s,
\qquad 0\leq s\leq1.
$$

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