Problem 1E
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) 
¼ 
¼ 
¼ 
1/4 
a. List all the different samples of n = 2 measurements that can be selected from this population.
b. Calculate the mean of each different sample listed in part a.
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?
d. Assume that a random sample of n = 2 measurements is selected from the population. List the different values of x̄found in part b and find the probability of each. Then give the sampling distribution of the sample mean x̄ in tabular form.
e. Construct a probability histogram for the sampling distribution of x̄.
Answer:
Step 1 of 6:
Given the probability distribution 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) 

Step 2 of 6:
a). To list all the different samples of n = 2 measurements that can be selected from this population.
The different samples of n = 2 with replacement and their means are:
Possible samples 
(0,0) 
(0,2) 
(0,4) 
(0,6) 
(2,0) 
(2,2) 
(2,4) 
(2,6) 
(4,0) 
(4,2) 
(4,4) 
(4,6) 
(6,0) 
(6,2) 
(6,4) 
(6,6) 
Step 3 of 6:
b). To calculate the mean of each different sample listed in part(a).
Possible samples 
Mean ( 
(0,0) 
0 
(0,2) 
1 
(0,4) 
2 
(0,6) 
3 
(2,0) 
1 
(2,2) 
2 
(2,4) 
3 
(2,6) 
4 
(4,0) 
2 
(4,2) 
3 
(4,4) 
4 
(4,6) 
5 
(6,0) 
3 
(6,2) 
4 
(6,4) 
5 
(6,6) 
6 