Deduce that Xr, given Xt = x, follows a lognormal distribution with mean E(Xr | Xt = x) = xell usds and variance Var(XT | Xt = x) = x2 (elt olds - 1)e2fil Heads (d) (5p) Ornstein-Uhlenbeck Process Suppose X, follows the Ornstein-Uhlenbeck process with SDE dXt = k(0 - Xt)dt + odW where k, 0, and o are constants. By applying Ito's formula to Y = ext X, and taking integrals show that for t