Question

An employee is selected from a staff of 10 to supervise a certain project by selecting a tag at random from a box containing 10 tags numbered from 1 to 10. Find the formula for the probability distribution of X representing the number on the tag that is drawn.

Find the mean and variance of the random variable X

Answer 1

An employee is selected from a staff of 10 to supervise a certain project by selecting a tag at random from a box containing 10 tags numbered from 1 to 10. Find the formula for the probability distribution of X representing the number on the tag that is drawn.

Find the mean and variance of the random variable X

Let random variable X represent the number of the drawn tag. Since the simple space consists of 10 equally likely events

$\Omega=\{1, 2, 3, 4 ,5 ,6 ,7 ,8 ,9 ,10\}$

thus the formula for probability distribution

$f(x)=\begin{cases} \frac{1}{10} \ for \ x=1, 2, ...,10\\ 0 \ elsewhere \end{cases}$

The mean:

$\mu=\sum x_i P(x_i)=0.1\cdot(1+2+3+4+5+6+7+8+9+10)=5.5$

Variance:

$var(x)=\sum(x_i-\mu)^2P(x_i)=0.1\cdot((1-5.5)^2+(2-5.5)^2+(3-5.5)^2+(4-5.5)^2+(5-5.5)^2+(6-5.5)^2+(7-5.5)^2+(8-5.5)^2+(9-5.5)^2+(10-5.5)^2)=0.1\cdot(20.25+12.25+6.25+2.25+0.25+0.25+2.25+6.25+12.25+20.25)=8.25$