Question

For the given probability distribution, find the mean and standard deviation.

   x    P(X=x)

   -1.5    0.3

   0    0.5

   2.75 0.1

5    0.1

Answer 1

Solution,

x	P(X = x)	x * P(X = x)	x2 *  P(X = x)
-1.5	0.3	-0.45	0.675
0	0.5	0	0
2.75	0.1	0.275	0.75625
5	0.1	0.5	2.5
	1	0.325	3.93125

mean = u = x * P(X = x) = 0.325

standard deviation =   x2 *  P(X = x) - ( u)2

= 3.93125 - ( 0.325)2

= 3.93125 - 0.105625

= 3.825625

standard deviation = 1.96