Question

The following table gives the probability distribution for a random variable X

x	P(x)
0	.028
1	.131
2	.261
3	.290
4	.194
5	.077
6	.017
7	.002

Find the mean and standard deviation of X.

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
0	0.028	0	0
1	0.131	0.131	0.131
2	0.261	0.522	1.044
3	0.29	0.87	2.61
4	0.194	0.776	3.104
5	0.077	0.385	1.925
6	0.017	0.102	0.612
7	0.002	0.014	0.098
Sum	1	2.8	9.524

Mean = X * P(X)

= 2.8

Standard deviation =

=X 2 * P(X) - 2

=  9.524 - (2.8)2 = 1.684

Standard deviation = = 1.2977