Question: Suppose X, X2,..., Xn is a random sample from a population with a mean of u and a standard deviation of o2. Suppose we

Suppose X, X2,..., Xn is a random sample from a population with

Suppose X, X2,..., Xn is a random sample from a population with a mean of u and a standard deviation of o2. Suppose we have an alternative estimator for the unknown population mean given by: = X + X2 + X3 3 We want to compare the two estimators: and the sample mean X (a) Is an unbiased estimator? Show your work. (b) Compare the mean of with the mean of X. Which estimator would you choose based on the mean? (c) Calculate the variance of X. (d) Compare the variance of with the variance of the sample mean X. (e) Which is a better estimator for ? or X ? Motivate your answer.

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