2. Three randomly selected households are surveyed. The numbersof people in the households are 1​, 4​, and 10. Assume that samplesof size n=2 are randomly selected with replacement from thepopulation of 1​, 4​, and 10. Listed below are the nine differentsamples. Complete parts​ (a) through​ (c).

Sample           x1        x2

1         1          1

2         1          4

3         1          10

4         4          1

5         4          4

6         4          10

7         10        1

8         10        4

9         10        10

a. Find the variance of each of the nine​samples, then summarize the sampling distribution of the variancesin the format of a table representing the probability distributionof the distinct variance values

                                   S^2                                                                     Probability

(4.5, 0,1)
(2.3,4.5,9)
(72,9,18)
(40.5,81,20.3)

​(Type an integer or a fraction. Use ascending order of thesample​ variances.)

b. Compare the population variance to the mean of the samplevariances. Choose the correct answer below.

A. The population variance is equal to the mean of the samplevariances.

B. The population variance is equal to the square of the mean ofthe sample variances.

C. The population variance is equal to the square root of themean of the sample variances.

c. Do the sample variances target the value of the population​variance? In​ general, do sample variances make good estimators ofpopulation​ variances? Why or why​ not?

A. The sample variances do not target the population​ variance,therefore, sample variances make good estimators of populationvariances.

B. The sample variances do not target the population​ variance,therefore, sample variances do not make good estimators ofpopulation variances.

C. The sample variances target the population​ variances,therefore, sample variances make good estimators of populationvariances.

D. The sample variances target the population​ variance,therefore, sample variances do not make good estimators ofpopulation variances.