B Let W And Z Be Independent Both Following A U 0 7 2 Distribution I Compute Essin W Z Using The 2nd Order Mome 1 (35.88 KiB) Viewed 88 times
B Let W And Z Be Independent Both Following A U 0 7 2 Distribution I Compute Essin W Z Using The 2nd Order Mome 2 (35.88 KiB) Viewed 88 times
(b) Let W and Z be independent both following a U(0,7/2) distribution. i. Compute Eſsin(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 Eſo(W)•()) as an integral. By considering the form of this integral, explain carefully why Elo(W)(2)) = E($(W)Ev(Z)]. (2) iii. Compute Eſsin(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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