a)
Since each sample is equally likely so probability of getting any sample is 1/9.
The variance of each sample is
Here X1 and X2 shows the observations of the samples. Following table shows the variances of samples and corresponding probabilities:
Samples | Variances,s^2 | P(s^2) | |
3 | 3 | 0 | 0.11111111 |
3 | 4 | 0.5 | 0.11111111 |
3 | 11 | 32 | 0.11111111 |
4 | 3 | 0.5 | 0.11111111 |
4 | 4 | 0 | 0.11111111 |
4 | 11 | 24.5 | 0.11111111 |
11 | 3 | 32 | 0.11111111 |
11 | 4 | 24.5 | 0.11111111 |
11 | 11 | 0 | 0.11111111 |
Following table shows the probability distribution of sample variances:
Variances,s^2 | P(s^2) |
0 | 0.3333 |
0.5 | 0.2222 |
24.5 | 0.2222 |
32 | 0.2222 |
b)
Following table shows the calculations for mean of population variances:
Variances,s^2 | P(s^2) | s^2P(s^2) |
0 | 0.3333 | 0 |
0.5 | 0.2222 | 0.1111 |
24.5 | 0.2222 | 5.4439 |
32 | 0.2222 | 7.1104 |
Total | 12.6654 |
So mean of sample variances is
The population variance is
Correct option is B.
c)
Correct option is D.
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selected households are surveyed. The numbers of people in the households are 3, 4, and 11....
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