Question

Given:

X F(X)

0 .3

1 .4

2 .1

3 .2

Find expected value of X. Find Standard Deviation of X

Answer 1

Solution:

x	P(X)	x*P(x)	x2	x2 * P(x)
0	0.3	0	0	0
1	0.4	0.4	1	0.4
2	0.1	0.2	4	0.4
3	0.2	0.6	9	1.8
Sum	1	1.2	14	2.6

Mean = E(X)

= Summation(x.P(X))

= 1.2

E(X) =  1.2

Now , E(X2) = summation [x2 * P(X)] = 2.6

Variance 2 = E(X2) - [E(x)]2

= 2.6 - [1.2]2

=  1.16

Now ,

Standard deviation =   =  1.16 =  1.0770

Standard deviation =  1.0770