Question

The number of books sold over the course of the five-day book fair were 2, 4, 6, 8, and 10. Assume that samples of size 2 are randomly selected with replacement from this population of five values List the different possible samples, and find the mean of each of them

Answer 1

When sampling with replacement, each draw is independent of the previous ones, and the same value can be drawn more than once.

The different possible samples of size 2 from the population {2, 4, 6, 8, 10} are as follows:

{2, 2}

{2, 4}

{2, 6}

{2, 8}

{2, 10}

{4, 2}

{4, 4}

{4, 6}

{4, 8}

{4, 10}

{6, 2}

{6, 4}

{6, 6}

{6, 8}

{6, 10}

{8, 2}

{8, 4}

{8, 6}

{8, 8}

{8, 10}

{10, 2}

{10, 4}

{10, 6}

{10, 8}

{10, 10}

Now, let's find the mean of each sample:

{2, 2} --> Mean = (2 + 2) / 2 = 2

{2, 4} --> Mean = (2 + 4) / 2 = 3

{2, 6} --> Mean = (2 + 6) / 2 = 4

{2, 8} --> Mean = (2 + 8) / 2 = 5

{2, 10} --> Mean = (2 + 10) / 2 = 6

{4, 2} --> Mean = (4 + 2) / 2 = 3

{4, 4} --> Mean = (4 + 4) / 2 = 4

{4, 6} --> Mean = (4 + 6) / 2 = 5

{4, 8} --> Mean = (4 + 8) / 2 = 6

{4, 10} --> Mean = (4 + 10) / 2 = 7

{6, 2} --> Mean = (6 + 2) / 2 = 4

{6, 4} --> Mean = (6 + 4) / 2 = 5

{6, 6} --> Mean = (6 + 6) / 2 = 6

{6, 8} --> Mean = (6 + 8) / 2 = 7

{6, 10} --> Mean = (6 + 10) / 2 = 8

{8, 2} --> Mean = (8 + 2) / 2 = 5

{8, 4} --> Mean = (8 + 4) / 2 = 6

{8, 6} --> Mean = (8 + 6) / 2 = 7

{8, 8} --> Mean = (8 + 8) / 2 = 8

{8, 10} --> Mean = (8 + 10) / 2 = 9

{10, 2} --> Mean = (10 + 2) / 2 = 6

{10, 4} --> Mean = (10 + 4) / 2 = 7

{10, 6} --> Mean = (10 + 6) / 2 = 8

{10, 8} --> Mean = (10 + 8) / 2 = 9

{10, 10} --> Mean = (10 + 10) / 2 = 10