Solve the following problem:
Q: A population consists of the four numbers {0, 2, 4, 6}. Consider drawing a random sample of size 2 with replacement.
(a) List all possible samples and evaluate for each.
(b) Determine the sampling distribution of X.
(c) Write down the population distribution and calculate its mean μ and standard deviation σ.
(d) Calculate the mean and standard deviation of the sampling distribution of X obtained in part (b), and verify that these agree with μ and σ √2 , respectively.