Question

Find the mean and standard deviation of each of the following probability distribution :

xi :	-3	-1	0	1	3
pi :	0.05	0.45	0.20	0.25	0.05

Answer 1

xi	pi	pixi	pixi2
-3	0.05	-0.15	0.45
-1	0.45	-0.45	0.45
0	0.20	0	0
1	0.25	0.25	0.25
3	0.05	0.15	0.45
		`∑`pixi = -0.2	`∑`pixi2=1.6

\[\text{ Mean }  = \sum p_i x_i = - 0 . 2\]
\[\text{ Variance }  = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean}  \right)^2 \]
\[ = 1 . 6 - \left( - 0 . 2 \right)^2 \]
\[ = 1 . 56\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance} }\]
\[ = \sqrt{1 . 56}\]
\[ = 1 . 249\]