(b) Let W and Z be independent both following a U(0,4/2) distribution. i. Compute Esin(W+Z)]...
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(b) Let W and Z be independent both following a U(0,4/2) distribution. i. Compute Esin(W+Z)] using the 2nd order moment approximation. Hint: write V = W + Z. What are E[V] and Var(V)? V [3] ii. For functions () and 4(.), write down the definition of E[(W)(Z)] as an integral. By considering the form of this integral, explain carefully why E[0(W)4(Z)] = E[0(W)]E[4(2)]. [2] iii. Compute Esin(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]
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