Chapter 6.2, Problem 14LM

a.

To determine

To find: The value of $\mu$ and ${\sigma }^2$.

b.

To determine

To find: The sampling distribution of the sample mean $\overline{x}$ for a random sample of $n=2$ measurements from this distribution.

c.

To determine

To show: Whether $\overline{x}$ is an unbiased estimator of $\mu$ or not.

d.

To determine

To find: The sampling distribution of sample variance $s^2$ of a random sample of $n=2$ measurements from this distribution.

e.

To determine

To show: Whether the sample variance $s^2$ is an unbiased estimator of ${\sigma }^2$ or not.