Solution Found!
Refer to Exercise 5.3.a. Find the sampling distribution of
Chapter 5, Problem 13E(choose chapter or problem)
Problem 13E
Refer to Exercise 5.3.
a. Find the sampling distribution of s2.
b. Find the population variance σ2.
c. Show that s2 is an unbiased estimator of σ2.
d. Find the sampling distribution of the sample standard deviation s.
e. Show that s is a biased estimator of σ.
Questions & Answers
QUESTION:
Problem 13E
Refer to Exercise 5.3.
a. Find the sampling distribution of s2.
b. Find the population variance σ2.
c. Show that s2 is an unbiased estimator of σ2.
d. Find the sampling distribution of the sample standard deviation s.
e. Show that s is a biased estimator of σ.
ANSWER:
Solution
Step 1 of 5
a) We have to find the sampling distribution of s2
From the data given in exercise we have find s2
Now calculate the s2 values for each sample
For the sample (1,1)
Then s2 =[(1-1)2+(1-1)2]/1
=0
For the sample (1,2)
Then s2 =[(1-15)2+(2-1.5)2]/1
=0.5
Calculate the s2 values for all the remaining samples
s2 |
p(s2) |
s2 |
p(s2) |
0 |
0.04 |
0.5 |
0.04 |
0.5 |
0.06 |
2 |
0.02 |
2 |
0.04 |
4.5 |
0.04 |
4.5 |
0.04 |
2 |
0.06 |
8 |
0.02 |
0.5 |
0.04 |
0.5 |
0.06 |
0 |
0.04 |
0 |
0.09 |
0.5 |
0.02 |
0.5 |
0.06 |
8 |
0.02 |
2 |
0.06 |
4.5 |
0.03 |
4.5 |
0.03 |
2 |
0.02 |
2 |
0.04 |
0.5 |
0.02 |
0.5 |
0.06 |
0 |
0.01 |
0 |
0.04 |
Now the sampling distribution of s2 is
s2 |
0 |
0.5 |
2 |
4.5 |
8 |
p(s2) |
0.22 |
0.36 |
0.24 |
0.14 |
0.04 |