Question

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

xi :	1	2	3	4
pi :	0.4	0.3	0.2	0.1

Answer 1

xi	pi	pixi	pixi2
1	0.4	0.4	0.4
2	0.3	0.6	1.2
3	0.2	0.6	1.8
4	0.1	0.4	1.6
		`∑`pixi = 2	`∑`pixi2=5

\[\text{ Mean } = \sum p_i x_i = 2\]
\[\text{ Variance } = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean}  \right)^2 \]
\[ = 5 - 2^2 \]
\[ = 1\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance } }\]
\[ = \sqrt{1}\]
\[ = 1\]