Let (0, F, P) be a probability space and let {Wt : t 2 0} be a standard Wiener process. Suppose Xt follows the Brownian bridge process with SDE dx - y- Xt 1 - t dt + dWt, X1 = y, where the diffusion is conditioned to be at y at time t = 1. (i) (10p) By applying Taylor's formula to Yt = and taking integrals, show that under an initial condition Xo = x, for 0