Question

Solve for the mean and the variance of the discrete random variable x wich can take only the values 2,4,5 and 9 given that P(2) =9/20, P(4) =1/20, P(5) = 1/5 and P(9)= 3/10

Answer 1

The mean:

$\mu=\sum x_i\cdot P(x_i)=\\ =2\cdot\cfrac{9}{20}+4\cdot\cfrac{1}{20}+5\cdot\cfrac{1}{5}+9\cdot\cfrac{3}{10}=4.8.$

The variance:

$\sigma^2=\sum(x_i-\mu)^2\cdot P(x_i),$

$X-\mu=\begin{Bmatrix} 2-4.8, 4-4.8, 5-4.8, 9-4.8 \end{Bmatrix}=$

$=\begin{Bmatrix} -2.8, -0.8, 0.2, 4.2 \end{Bmatrix},$

$\sigma^2=(-2.8)^2\cdot \cfrac{9}{20}+(-0.8)^2\cdot \cfrac{1}{20}+0.2^2\cdot \cfrac{1}{5}+4.2^2\cdot \cfrac{3}{10}=8.86.$