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In: Statistics and Probability

For the following symmetric populations and odd sample size n = 2m + 1, derive the...

For the following symmetric populations and odd sample size n = 2m + 1, derive the asymptotic distributions of the sample mean and sample median, calculate the asymptotic relative efficiency of the median to the mean and identify which is more efficient.

(a) Normal(μ,σ2)

(b) Uniform(0,β)

(c) Beta(α,α)

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