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  3. 3 suppose we observe 5 values from an unknown distribution...

Question: 3 suppose we observe 5 values from an unknown distribution...

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3. Suppose we observe 5 values from an unknown distribution: (1,7,5, 16,4). (a) Find the sample mean (which is often used as an estimator of the population mean) (b) Find the sample variance (which is often used as an estimator of the population variance). (c) In general, the estimators above are both unbiased and consistent for the population mean and variance, respectively Bias and consistency are both measures of the central tendency of an estimators. One is more relevant in large samples, the other in small samples. Which is which? Explain. (d) Suppose we know that the 5 values are from a symmetric distribution. Then the sample median is also unbiased and consistent for the population mean. The sample mean has lower variance. Would you prefer to use the sample mean or sample median as an estimator of the population mean? Why?

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