2 Let $ X(t) t 0 be a Brownian motion with variance parameter 2 Show that, for all t 0, X(t) and max 0st X(s) are identically distributed

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Question: 2. Let $ X(t): t 0 % be a Brownian motion with variance parameter 2. Show that, for all t > 0, |X(t)| and

2. Let $ X(t): t ≥ 0 % be a Brownian motion with variance parameter σ2. Show that, for all t > 0, |X(t)| and max 0≤s≤t X(s) are identically distributed.

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