Question

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

xi :	-2	-1	0	1	2
pi :	0.1	0.2	0.4	0.2	0.1

Answer 1

xi	pi	pixi	`∑`pixi2
-2	0.1	-0.2	0.4
-1	0.2	-0.2	0.2
0	0.4	0	0
1	0.2	0.2	0.2
2	0.1	0.2	0.4
		`∑`pixi = 0	`∑`pixi2 = 1.2

\[\text{ Mean }  = \sum p_i x_i = 0\]
\[\text{ Variance } = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean}  \right)^2 \]
\[ = 1 . 2 - 0^2 \]
\[ = 1 . 2\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance } } \]
\[ = \sqrt{1 . 2}\]
\[ = 1 . 095\]