Chapter 5.2, Problem 5.9LM

Consider the following probability distribution:

x	2	4	9
p(x)	$\frac{1}{3}$	$\frac{1}{3}$	$\frac{1}{3}$

1. a. Calculate µ for this distribution.
2. b. Find the sampling distribution of the sample mean $\bar{x}$ for a random sample of n = 3 measurements from this distribution, and show that $\bar{x}$ is an unbiased estimator of µ.
3. 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 µ.
4. d. If you wanted to use a sample of three measurements from this population to estimate µ, which estimator would you use? Why?