Question

A population consists of the five measurements 2, 6, 8, 3 & 1. How many different

samples of size n = 2 can be drawn from the population? What is the mean & variance

of the sampling distribution of the sample means? Follow steps 1 to 6.

Answer 1

$EX=\frac{2+6+8+3+1}{5}=4\\EX^2=\frac{2^2+6^2+8^2+3^2+1^2}{5}=22.8\\DX=EX^2-\left( EX \right) ^2=22.8-4^2=6.8\\E\bar{x}=EX=4\\D\bar{x}=\frac{DX}{2}=\frac{6.8}{2}=3.4\\$