Answer to Question #211158 in Statistics and Probability for riri

Question

A population consist of the four numbers 1, 2, 4 and 5. List all the possible samples of size n=3 which can be drawn with replacement from population

Answer 1

We have population values $1,2,4,5$ population size $N=4$ and sample size $n=3.$Thus, the number of possible samples which can be drawn with replacement is

$$(N)^n=4^3=64$$

2.

$$\def\arraystretch{1.5} \begin{array}{c:c} Sample & Sample \\ No. & values & (\bar{X}) \\ \hline 1 & 1,1,1 \\ \hdashline 2 & 1,1,2 \\ \hdashline 3 & 1,1,4 \\ \hdashline 4 & 1,1.5 \\ \hdashline 5 & 1,2,1 \\ \hdashline 6 & 1,2,2 \\ \hline 7 & 1,2,4 \\ \hline 8 & 1,2,5 \\ \hline 9 & 1,4,1 \\ \hline 10 & 1,4,2 \\ \hline 11 & 1,4,4 \\ \hline 12 & 1,4,5 \\ \hline 13 & 1,5,1 \\ \hline 14 & 1,5,2 \\ \hline 15 & 1,5,4 \\ \hline 16 & 1,5,5 \\ \hline 17 & 2,1,1 \\ \hdashline 18 & 2,1,2 \\ \hdashline 19 & 2,1,4 \\ \hdashline 20 & 2,1.5 \\ \hdashline 21 & 2,2,1 \\ \hdashline 22 & 2,2,2 \\ \hline 23 & 2,2,4 \\ \hline 24 & 2,2,5 \\ \hline 25 & 2,4,1 \\ \hline 26 & 2,4,2 \\ \hline 27 & 2,4,4 \\ \hline 28 & 2,4,5 \\ \hline 29 & 2,5,1 \\ \hline 30 & 2,5,2 \\ \hline 31 & 2,5,4 \\ \hline 32 & 2,5,5 \\ \hline 33 & 4,1,1 \\ \hdashline 34 & 4,1,2 \\ \hdashline 35 & 4,1,4 \\ \hdashline 36 & 4,1.5 \\ \hdashline 37 & 4,2,1 \\ \hdashline 38 & 4,2,2 \\ \hline 39 & 4,2,4 \\ \hline 40 & 4,2,5 \\ \hline 41 & 4,4,1 \\ \hline 42 & 4,4,2 \\ \hline 43 & 4,4,4 \\ \hline 44 & 4,4,5 \\ \hline 45 & 4,5,1 \\ \hline 46 & 4,5,2 \\ \hline 47 & 4,5,4 \\ \hline 48 & 4,5,5 \\ \hline 49 & 5,1,1 \\ \hdashline 50 & 5,1,2 \\ \hdashline 51 & 5,1,4 \\ \hdashline 52 & 5,1.5 \\ \hdashline 53 & 5,2,1 \\ \hdashline 54 & 5,2,2 \\ \hline 55 & 5,2,4 \\ \hline 56 & 5,2,5 \\ \hline 57 & 5,4,1 \\ \hline 58 & 5,4,2 \\ \hline 59 & 5,4,4 \\ \hline 60 & 5,4,5 \\ \hline 61 & 5,5,1 \\ \hline 62 & 5,5,2 \\ \hline 63 & 5,5,4 \\ \hline 64 & 5,5,5 \\ \hline \end{array}$$