Homework 1
1. Consider the following probability distribution
a. List all the different samples of n=2 measurements that can be selected from this
Population.
Possible Samples:
1.
0,0
9.
4,0
2.
0,2
10.
4,2
3.
0,4
11.
4,4
4.
0,6
12.
4,6
5.
2,0
13.
6,0
6.
2,2
14.
6,2
7.
2,4
15.
6,4
8.
2,6
16.
6,6
b. Calculate the mean of each different sample.
Mean of each Sample
(
?
):
̅
1.
(0+0)/2=0
9.
(4+0)/2=2
2.
(0+2)/2=1
10.
(4+2)/2=3
3.
(0+4)/2=2
11.
(4+4)/2=4
4.
(0+6)/2=3
12.
(4+6)/2=5
5.
(2+0)/2=1
13.
(6+0)/2=3
6.
(2+2)/2=2
14.
(6+2)/2=4
7.
(2+4)/2=3
15.
(6+4)/2=5
8.
(2+6)/2=4
16.
(6+6)/2=6
c. Of a sample of n=2 measurements is randomly selected from the population, what
is the probability that a specific sample will be selected?
Probability of specific Sample:
1.
0,0= 1/6
9.
4,0= 1/6
2.
0,2= 1/6
10.
4,2= 1/6
3.
0,4= 1/6
11.
4,4= 1/6
4.
0,6= 1/6
12.
4,6= 1/6
5.
2,0= 1/6
13.
6,0= 1/6
6.
2,2= 1/6
14.
6,2= 1/6
7.
2,4= 1/6
15.
6,4= 1/6
8.
2,6= 1/6
16.
6,6= 1/6
d. Assume that a random sample of n=2 measurements is selected from a population.
List the different values of
?
and find the probability of each. Then give the sampling
̅
distribution of the sample mean
?
in tabular form.
̅
Probability of
?