Consider the following probability distribution: x 2 4 9 p1x2 1 3 1 3 1 3

a. Calculate m for this distribution.

b. Find the sampling distribution of the sample mean x for a random sample of n = 3 measurements from this distribution, and show that x is an unbiased estimator of m.

c. Find the sampling distribution of the sample median m for a random sample of n = 3 measurements from this distribution, and show that the median is a biased estimator of m. NW

d. If you wanted to use a sample of three measurements from this population to estimate m, which estimator would you use? Why?