Question

4. Xi ,i = 1, , n are iid N(μ, σ2). (a) Find the MLE of μ, σ2. Are these unbiased estimators of μ and of σ2 respectively? Aside: You can use your result in (b) to justify your answer for the bias part of the MLE estimator of σ2 (b) In this part you will show, despite that the sample variance is an unbiased estimator of σ2, that the sample standard deviation is is a biased estimator of σ. This fills in some parts of a comment in the lectures. n. i-1 State an appropriate result from Chapter 6 of the text which gives the distribution of (n 1)S2/2 Use this to find E(S2)

Answer 1

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E(x) = n h-I h-I

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