Question

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

xi :	2	3	4
pi :	0.2	0.5	0.3

 

Answer 1

xi	pi	pixi	pixi2
2	0.2	0.4	0.8
3	0.5	1.5	4.5
4	0.3	1.2	4.8
		`∑`pixi = 3.1	`∑`pixi2 = 10.1

\[\text{ Mean }  = \sum p_i x_i = 3 . 1\]
\[\text{ Variance}  = \sum p_i {x_i}^2 - \left( \text{ Mean}  \right)^2 \]
\[ = 10 . 1 - \left( 3 . 1 \right)^2 \]
\[ = 10 . 1 - 9 . 61\]
\[ = 0 . 49\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance}}\]
\[ = \sqrt{0 . 49}\]
\[ = 0 . 7\]