Let X1, ,Xn be a random sample from N(,2) distribution with both parameters unknown Let L be the length of the shortest confidence interval for on confidence level 1 (i) Find E(L2 ) as a function of n,2 and (ii) Find the smallest n such that E(L2 ) 2 2 for a given

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Question: Let X1, ...,Xn be a random sample from N(,2) distribution with both parameters unknown. Let L be the length of the shortest confidence interval for

Let X1, ...,Xn be a random sample from N(μ,σ2) distribution with both parameters unknown. Let Lα be the length of the shortest confidence interval for μ on confidence level 1 − α. (i) Find E(L2

α) as a function of n,σ2 and α. (ii) Find the smallest n such that E(L2

α) ≤ σ2/2 for a given α.

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