For samples of three independent observations from the distribution given in Exercise 11, find (by enumeration) the sampling distribution of the sample variance (s2), the modified sample variance (s2), and the sample range (the difference between the largest and smallest values in the sample).

(a) Is the sample range unbiased as an estimator of the population variance?

(b) Compute the mean-square errors of the three sample statistics (s2, s2, and the sample range). Which of the three statistics has the smallest mean-square error as an estimator of the population variance?