Question

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

xi:	0	1	3	5
pi :	0.2	0.5	0.2	0.1

Answer 1

xi	pi	pixi	pixi2
0	0.2	0	0
1	0.5	0.5	0.5
3	0.2	0.6	1.8
5	0.1	0.5	2.5
		`∑`pixi = 1.6	`∑`pixi2=4.8

\[\text{ Mean }  = \sum p_i x_i = 1 . 6\]
\[\text{ Variance } = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean }  \right)^2 \]
\[ = 4 . 8 - 1 . 6^2 \]
\[ = 2 . 24\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance} }\]
\[ = \sqrt{2 . 24}\]
\[ = 1 . 497\]