Question: 4. Let X1,X2, . . . ,Xn be a random sample of size n from the exponential distribution with parameter A such that the mean

4. Let X1,X2, . . . ,Xn be a random sample of size n from the exponential distribution with parameter A such that the mean and the variance of Xi are A and A2, respectively. Let X be the corresponding sample mean. (a) (2 marks) When n is large, what is the approximate distribution of Z = 5991? Why? (b) (6 marks) Derive a 100(1 01)% two-sided condence interval for A based on Z. (c) (6 marks) It can be shown that AX follows Gamma(n, n) Use this fact to nd a pivotal quantity and provide a 100(1 00% twosided condence interval for A

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