4 Let $ X(t) t 0 be a Brownian motion with variance parameter 2 Let T be the time of hitting first Let Y N (0, 2 2) Show that, for 0, T and 1 Y 2 are identically distributed

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Question: 4. Let $ X(t): t 0 % be a Brownian motion with variance parameter 2. Let T be the time of hitting first.

4. Let $ X(t): t ≥ 0 % be a Brownian motion with variance parameter σ2. Let Tα be the time of hitting α first. Let Y ∼ N (0, σ2/α2). Show that, for α > 0, Tα and 1/Y 2 are identically distributed.

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