Question: X1, X2, .., Xa is a random sample from a normal distribution with mean and variance 2. Let Xmin and Xmax be the smallest and

X1, X2, .., Xa is a random sample from a normal with mean and variance σ2. Let Xmin and Xmax be the smallest and largest observations in the sample. (a) Is (Xmin + X man)/2) an unbiased estimate for μ? (b) What is the standard error of this estimate? (c) Would this estimate be preferable to the sample mean X?

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