Question

A population is given by 5 8 10 15 16 20 draw all possible samples of size 2 without replacement. Show that E(x ̅ )=μ

Answer 1

N=6

n=2

$\mu = \frac{5+ 8+ 10+ 15+ 16+ 20}{6} = 12.33$

Number of samples $= \frac{6!}{2!(6-2)!} = \frac{5 \times 6}{2} = 15$

$E(\bar{x}) = \frac{6.5+7.5+...+17.5+18}{15}=12.33$