Answer to Question #197548 in Statistics and Probability for joshua

Question

A discrete uniform population consists of the values 0,1,2, and 3. Suppose you have a sample size of 2 without replacement, find population and sample mean, variance, and standard deviation.

Answer 1

$Number = \frac{N!}{n!(N-n)!} \\ = \frac{4!}{2!(4-2)!} \\ = \frac{3 \times 4}{2} \\ = 6$

samples:

0, 1

0, 2

0, 3

1, 2

1, 3

2, 3

Population mean $= \frac{0+1+2+3}{4}=1.5$

Population variance $= \frac{1}{4-1}( (0-1.5)^2+(1-1.5)^2 +(2-1.5)^2 +(3-1.5)^2 )$

$= \frac{1}{3}(2.25+0.25+0.25+2.25) = 1.667$

Population standard deviation $= \sqrt{1.667}=1.29$