Answer to Question #322869 in Statistics and Probability for Hanz

Question

A population consist of three numbers 3,4,8.Consider all possible samples of size 2 which can be drawn with replacement from the population.Find the following population mean, population variance, population standard deviation

Answer 1

$Samples:\\\left( 3,3 \right) ,\left( 3,4 \right) ,\left( 3,8 \right) \\\left( 4,3 \right) ,\left( 4,4 \right) ,\left( 4,8 \right) \\\left( 8,3 \right) ,\left( 8,4 \right) ,\left( 8,8 \right) \\\mu =\frac{3+4+8}{3}=5\\\sigma ^2=\frac{\left( 3-5 \right) ^2+\left( 4-5 \right) ^2+\left( 8-5 \right) ^2}{3}=4.66667\\\sigma =\sqrt{\sigma ^2}=\sqrt{4.66667}=2.16025$