A population consists of the five numbers 2, 3, 6, 8, and 11.
Consider the samples of size 2 that can be drawn from this
population.
A. List all the possible samples and the corresponding mean.
B. Construct the sampling distribution of the sample mean.
1 -- All possible samples and their means:
2 -- Sampling distribution of the sample mean:
"\\def\\arraystretch{1.5} \\begin{array}{c:c:c:c:c:c:c} & \\bar{X} & f & f(\\bar{X}) & Xf(\\bar{X})& X^2f(\\bar{X}) \\\\ \\hline & 2.5 & 1 & 0.1 & 0.25 & 0.625\\\\ \\hdashline & 4 & 1 & 0.1 & 0.4 & 1.6 \\\\ \\hdashline & 5 & 1 & 0.1 & 0.5 & 2.5\\\\ \\hdashline & 6.5 & 1 & 0.1 & 0.65 & 4.225 \\\\ \\hdashline & 4.5& 1 & 0.1 & 0.45 & 2.025 \\\\ \\hdashline & 5.5 & 1 & 0.1 & 0.55 & 3.025 \\\\ \\hdashline & 7 & 2 & 0.2& 1.4 & 9.8 \\\\ \\hdashline & 8.5 & 1 & 0.1& 0.85 & 7.225 \\\\ \\hdashline & 9.5 & 1 & 0.1 & 0.95 & 9.025 \\\\ \\hdashline Total= & & 10 & 1 & 6 & 40.05 \\\\ \\hdashline \\end{array}"
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