Question

Random samples of size 4 are drawn, with replacement, from the finite population 2, 4, and 6.N (a) Assuming that the SI possible samples are all equally likely to occur, con struct the sampling distribution of X.

Answer 1

The sampling distribution of the mean (X) when random samples of size 4 are drawn, with replacement, from the population of 2, 4, and 6 is {2, 4, 6} with equal probabilities.

Step-by-step explanation:

The question is asking about the sampling distribution of the mean (X) when random samples of size 4 are drawn, with replacement, from the finite population of 2, 4, and 6.

If we assume all possible samples are equally likely to occur, we can construct the sampling distribution of X.

Since there are only three numbers in the population, the sampling distribution of X will have three possible values: X = (2+2+2+2)/4 = 2, X = (4+4+4+4)/4 = 4, and X = (6+6+6+6)/4 = 6.

Each of these possible values has equal probability of occurring, so the sampling distribution of X is {2, 4, 6} with equal probabilities.