1) Suppose dX = (X + X1/2) dt + X1.5 dW. Find the Partial Differential Equation (PDE) and terminal condition that g(x,t) = E[e-r(T-t) {log(X(T))-sin( X(T)} |Ft] satisfies. 2) Suppose X follows an Arithmetic Brownian Motion. Find the PDE that g(x,t) = E[3e2X(T) | Ft] satisfies and solve it. (Hint: Use the ansatz g(x,t) = b(t)e2x ) 3) Suppose X follows a Geometric Brownian Motion. Find the PDE that g(x,t) = E[e-r(T-t)(X(T) + 2X(T)2 + 3X(T)3) | Ft] satisfies and solve it. (Hint: Split the expectation into the sum of 3 expectations then create and solve an ansatz for each expectation.) If you can't solve this all the way get as far as you can