Question

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

xi :	−1	0	1	2	3
pi :	0.3	0.1	0.1	0.3	0.2

Answer 1

xi	pi	pixi	pixi2
-1	0.3	-0.3	0.3
0	0.1	0	0
1	0.1	0.1	0.1
2	0.3	0.6	1.2
3	0.2	0.6	1.8
		`∑`pixi = 1	`∑`pixi2=3.4

\[\text{ Mean }  = \sum p_i x_i = 1\]
\[\text{ Variance }  = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean }  \right)^2 \]
\[ = 3 . 4 - 1\]
\[ = 2 . 4\]
\[\text{ Step Deviation }  = \sqrt{\text{ Variance} }\]
\[ = \sqrt{2 . 4}\]
\[ = 1 . 549\]