Question: Q3 Problem 2 30 Points 2. Let X1, . .., Xn be a random sample with common mean E[X] = ke and variance Var(X) =

Q3 Problem 2 30 Points 2. Let X1, . .., Xn be a random sample with common mean E[X"] = ke and variance Var(X) = k02 where k, 0 > 0 are the parameters. Q3.1 Part 1 20 Points (a) (10 pts) Suppose that k is known. Find an approximate (1 - a)-level confidence interval for 0 by using a pivot of the form Vn(X - ke) g(X1, . . ., Xn) for some function g if n is large. Hint: g(X1, ..., X,) is either Xn or ! )_, (X - Xn)2. Specify L(X1, . . ., Xn), U(X 1, . . ., Xn). (b) (10 pts) Find an approximate (1 - o)-level confidence interval for E[X] = ke by using a pivot of the form Vn(Xn - ke) g(X1, . . . , Xn) for some function g if n is large. Hint: g(X1, ..., X,) is either Xn or ! _, (X, - Xn)2. Specify L(X1, . .., X), U(X1, . . ., X.). Please select file(s) Select file(s) Q3.2 Part 2 10 Points (c) (10 pts) Suppose that & is known. Use a variance stabilizing transformation to find an approximate (1-o)-level confidence interval for k. Specify L(X1, . ... Xn), U(X1, .. . . Xn)

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