Chapter 5.1, Problem 5.1LM

The probability distribution shown here describes a population of measurements that can assume values of 0, 2, 4, and 6, each of which occurs with the same relative frequency:

x	0	2	4	6
p(x)	$\frac{1}{4}$	$\frac{1}{4}$	$\frac{1}{4}$	$\frac{1}{4}$

1. a. List all the different samples of n = 2 measurements that can be selected from this population. For example, (0, 6) is one possible pair of measurements; (2, 2) is another possible pair.
2. b. Calculate the mean of each different sample listed in part a.
3. c. If a sample of n = 2 measurements is randomly selected from the population, what is the probability that a specific sample will be selected?
4. d. Assume that a random sample of n = 2 measurements is selected from the population. List the different values of $\bar{x}$ found in part b and find the probability of each. Then give the sampling distribution of the sample mean $\bar{x}$ in tabular form.
5. e. Construct a probability histogram for the sampling distribution of $\bar{x}$.