Answer to Question #289012 in Statistics and Probability for lusientoo

Question

A box contains 5 balls. One is numbered 1, two are numbered 2, and two are numbered 3. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the standard deviation of the numbers on the balls

Answer 1

Let X be a random variable represents the number on the ball, then

$P(X=1)=0.2$

$P(X=2)=0.4$

$P(X=3)=0.4$

$\sigma=\sqrt{D}=\sqrt{M(X^2)-M^2(X)}$

$M(X)=1*0.2+2*0.4+3*0.4=2.2\implies M^2(X)=4.84$

$M(X^2)=1^2*0.2+2^2*0.4+3^2*0.4=5.4$

So, $\sigma=\sqrt{5.4-4.84}=\sqrt{0.56}\approx0.75$