Let {X(t), t > 0} be a standard Brownian motion process and Ta denote the first...

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Let {X(t), t > 0} be a standard Brownian motion process and Ta denote the first time the process hits a. (a) Show that E[X(t)|X(u),0 < u < s] = X(s) for s <t. (b) Solve for Pr (T–1 < T1 < T_2 < T2). Let {X(t), t > 0} be a standard Brownian motion process and Ta denote the first time the process hits a. (a) Show that E[X(t)|X(u),0 < u < s] = X(s) for s <t. (b) Solve for Pr (T–1 < T1 < T_2 < T2).