Unbiased and Biased Estimators. A statistic is said to be an unbiased estimator of a parameter if the mean of all its possible values equals the parameter; otherwise, it is said to be a biased estimator. An unbiased estimator yields, on average, the correct value of the parameter, whereas a biased estimator does not.

a. Is the sample mean an unbiased estimator of the population mean?

Explain your answer.

b. Is the sample median an unbiased estimator of the population median? (Hint: Refer to Example 7.2 on pages 331–332. Consider samples of size 2.)

For Exercises 7.55–7.57, refer to Equations (7.1) and (7.2) on pages 337 and 338, respectively.