Consider the following probability distribution: x 0 1 4 p1x2 1 3 1 3 1 3

a. Find m and s2 .

b. Find the sampling distribution of the sample mean x for a random sample of n = 2 measurements from this distribution.

c. Show that x is an unbiased estimator of m. [Hint: Show that E1x2 = Σxp1x2 = m.]

d. Find the sampling distribution of the sample variance s2 for a random sample of n = 2 measurements from this distribution.

e. Show that s2 is an unbiased estimator for s2 .