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W is a standard Brownian motion. Compute E[W(T) exp(W(T))].

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Let W be standard Brownian motion and define the Brownian bridge X_t = W_t - t W_1 on [0,1]. Compute E[X_{1/2} | X_{3/4} = 3].S_t follows dS = 3 S dt + 4 S dW with W a standard Brownian motion. Find the dynamics of X_t = ln S_t in the form dX = a dt + b dW.

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