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A medical variable is believed to be normally distributed. Knowing the mean tells whether a certain medicine is e'ective. The mean ,u is unknown and...

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sample mean, minimum variance unbiased estimator, standard error, mean squared error

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A medical variable is believed to be normally distributed. Knowing the mean tells whether a certain medicine is
efi'ective. The mean ,u is unknown and needs to be estimated. It’s time consuming to do experiments and get an
observation for this variable. A medical student plans to spend a month to get a rand_om sample of size 4: {X 1, X 2, X 3, X4}. Denote the standard deviation of the distribution by a, the sample mean by X4, the sample variance
_ 2 by 33 =; ‘=1(X" 4(4) . 1. Is the sample mean it. a random variable? If so, what’s its sampling distribution? 2. Is E. a MVUE (minimum variance unbiased estimator) of pt? 3. What's the standard error of It}? What’s the mean square error of £4 for estimating pt?

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