Question

A population consists of three numbers (3,4,7). Consider all possible samples of size 2 which can be drawn from the population. Find the variance of the sampling distribution of the sample means.

Answer 1

$\mu(3,4)=(3+4)/2=3.5$

$\mu(3,7)=(3+7)/2=5$

$\mu(4,7)=(4+7)/2=5.5$

f(3.5)=f(5)=f(5.5)=1/3

$E(x)=\sum fx=1/3(3.5+5+5.5)=4.7$

$\sigma^2=\sum fx^2-(\sum fx)^2=1/3(12.25+25+30.25)-22.09=0.41$