Question

Consider a population of 2,3,and 4 .suppose samples of size 2 are drawn from this population.describe the sampling distribution of the sample means.

What is the mean and variance of the sampling distribution of the sample means?

Answer 1

$\mu(2,3)=2.5$

$\mu(2,4)=3$

$\mu(3,4)=3.5$

f(2.5)=f(3)=f(3.5)=1/3

$E(x)=\sum fx=1/3(2.5+3+3.5)=3$

$\sigma^2=\sum fx^2- (\sum fx)^2 =1/3(6.25+9+12.25)-9=0.17$