Questions (a) and (b) are based on the following random sample of 12 data points from a population distribution : 7, 15, 15, 19, 26, 27, 29, 29, 30, 33, 38, 53.

(a) Find both the biased and the unbiased sample variances.

(b) Suppose that the distribution variance is 100.

- Find the mean square error of the sample mean as an estimator of the distribution mean.

- Find the bias in the biased form of the sample variance as an estimator of the distribution variance