Question

 A population consists of four members {3, 8, 10, 15}. Consider all possible samples of size 2 that can be drawn with replacement from the population

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} & 3 & 8 & 10 & 15 \\ \hline 3 & (3,3) & (3, 8) & (3, 10) & (3,15) \\ \hdashline 8 & (8,3) & (8, 8) & (8, 10) & (8,15) \\ \hdashline 10 & (10,3) & (10, 8) & (10, 10) & (10,15) \\ \hdashline 15 & (15,3) & (15, 8) & (15, 10) & (15,15) \end{array}$$

$$S=\{(3, 3), (3, 8), (3, 10), (3, 15),$$

$$(8, 3), (8, 8), (8, 10), (8, 15),$$

$$(10, 3), (10, 8), (10, 10), (10, 15),$$

$$(15, 3), (15, 8), (15, 10), (15, 15)\}$$