Three randomly selected households are surveyed the numbers of people in the households are 2, 6 and 7 assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 6 and 7 listed below are the nine different samples

2, 2 2,6 2,7 6,2 6,6 6,7 7,2 7,6 7,7

Find the variance of each of the nine samples then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values

S^2___________________ Probability

0, 0.3, or 0.3 ...............................

1, 6.3 or 0.5 ................................

8, 4 or 25 ..................................

40.5, 6.3 or 12.5 ..........................