Exercise 13.4 Let X], ..., X, be independent random variables with expected values E[X,] = /;, and consider the following simulation estimator of E[Y]: n W = Y+> ci(Xi -Hi). i=1 (a) Show that n n Var (W ) = Var(Y) + > c? Var(X,) + 2 ) c; Cov(Y, X;). i=1 1=1 (b) Use calculus to show that the values of c, ..., c, that minimize Var(W) are Cov(Y, Xi) C= i = 1, . ..,n. Var (Xi)Exercise 13.4 Let X], ..., X, be independent random variables with expected values E[X,] = /;, and consider the following simulation estimator of E[Y]: n W = Y+> ci(Xi -Hi). i=1 (a) Show that n n Var (W ) = Var(Y) + > c? Var(X,) + 2 ) c; Cov(Y, X;). i=1 1=1 (b) Use calculus to show that the values of c, ..., c, that minimize Var(W) are Cov(Y, Xi) C= i = 1, . ..,n. Var (Xi)