Question

Determine if the distribution represents a probability distribution. Then find Mean, Variance, and Standard Deviation. X 7 8 9 10 11 P(x) 0.3 0.5 0.1 0.08 0.02

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
7	0.3	2.1	14.7
8	0.5	4	32
9	0.1	0.9	8.1
10	0.08	0.8	8
11	0.02	0.22	2.42
Sum	1	8.02	65.22

Mean = X * P(X)

= 8.02

Variance

= X 2 * P(X) - 2

= 65.22 - (8.02)2 = 0.8996

Standard deviation = = 0.9484