(10%) Assume X(t) is a Brownian motion with variance parameter o = 1. (a). Let W = S+ X(s)ds. Calculate E(W2) under the condition that X(t) is a standard Brownian motion. (b). For a > 0,6 > 0, calculate P(X(T) is zero for at least one TE (0,t)|X(O) = a, X(t) = b). (10%) Assume X(t) is a Brownian motion with variance parameter o = 1. (a). Let W = S+ X(s)ds. Calculate E(W2) under the condition that X(t) is a standard Brownian motion. (b). For a > 0,6 > 0, calculate P(X(T) is zero for at least one TE (0,t)|X(O) = a, X(t) = b)