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	${\displaystyle \frac{1}{4}}$	${\displaystyle -\frac{5}{4}}$	${\displaystyle \frac{25}{4}}$
-4	${\displaystyle \frac{1}{8}}$	${\displaystyle -\frac{4}{8}}$	${\displaystyle \frac{16}{8}}$
1	${\displaystyle \frac{1}{2}}$	${\displaystyle \frac{1}{2}}$	${\displaystyle \frac{1}{2}}$
2	${\displaystyle \frac{1}{8}}$	${\displaystyle \frac{2}{8}}$	${\displaystyle \frac{4}{8}}$
		${\displaystyle \sum }$pixi=1	$${\sum }_{}^{}$$pixi2=$$\frac{74}{8}$$

$$\text{ Mean }=\sum p_i{x}_i=-1$$
$$\text{ Variance }=\sum p_i{x}_i{2}_{}^{}-{\left(\text{ Mean }\right)}^2$$
$$=\frac{74}{8}-{(-1)}^2$$
$$=9.25-1$$
$$=8.25$$
$$\text{ Step Deviation }=\sqrt{\text{ Variance }}$$
$$=\sqrt{8.25}$$
$$=2.872$$