Question

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

xi :	-5	-4	1	2
pi :	\[\frac{1}{4}\]	\[\frac{1}{8}\]	\[\frac{1}{2}\]	\[\frac{1}{8}\]

 

Answer 1

xi	pi	pixi	pixi2
-5	`1/4`	`-5/4`	`25/4`
-4	`1/8`	`-4/8`	`16/8`
1	`1/2`	`1/2`	`1/2`
2	`1/8`	`2/8`	`4/8`
		`∑`pixi=1	\[\sum\nolimits_{}^{}\]pixi2=\[\frac{74}{8}\]

\[\text{ Mean }  = \sum p_i x_i = - 1\]
\[\text{ Variance }  = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean }  \right)^2 \]
\[ = \frac{74}{8} - \left( - 1 \right)^2 \]
\[ = 9 . 25 - 1\]
\[ = 8 . 25\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance } }\]
\[ = \sqrt{8 . 25}\]
\[ = 2 . 872\]