List all possible samples of size n = 3, with replacement, from the population {1, 3, 5}.

Question:

List all possible samples of size n = 3, with replacement, from the population {1, 3, 5}. Calculate the mean of each sample. Find the mean, variance, and standard deviation of the sample means. Compare your results with the mean μ = 3, variance σ2 = 8/3, and standard deviation σ = √8/3 ≈ 1.633 of the population.

a. Form all possible samples of size 3 and find the mean of each.

b. Make a probability distribution of the sample means and find the mean, variance, and standard deviation.

c. Compare the mean, variance, and standard deviation of the sample means with those of the population.

Distribution
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