(b) Let W and Z be independent both following a U(0, T /2) distribution. i. Compute E[sin(W + Z)] using the 2nd order moment approximation. Hint : write V = W + Z. What are E[V] and Var(V)? [3] ii. For functions (.) and (.), write down the definition of Eld(W) y(Z)] as an integral. By considering the form of this integral, explain carefully why Ed(W) y(Z)] = Ed(W ) ]E[y(Z)]. [2] iii. Compute E[sin(W + Z)] exactly. How accurate is the 2nd-order moment approximation from part (b)i compared to the one in part (a)? Hint: Re- membering trigonometric identities will help you use the result from part (b)ii here. [3]