Question

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

xi :	1	3	4	5
pi:	0.4	0.1	0.2	0.3

 

Answer 1

xi	pi	pixi	pixi2
1	0.4	0.4	0.4
3	0.1	0.3	0.9
4	0.2	0.8	3.2
5	0.3	1.5	7.5
		`∑` pixi = 3	`∑`pixi2=12

\[\text{ Mean }  = \sum p_i x_i = 3\]
\[\text{ Variance } = \sum p_i {x_i}^2{}_{} - \left( \text{ Mean}  \right)^2 \]
\[ = 12 - 3^2 \]
\[ = 3\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance}}\]
\[ = \sqrt{3}\]
\[ = 1 . 732\]