Question

You are given the probability distribution below:

x	0	1	2	3	4
p(x)	0.05	0.35	0.25	0.20	0.15

Determine the standard deviation of X. Report your answer to three decimal places.

Answer 1

Solution:

We have

Mean = ∑XP(X)

Variance = ∑ P(X)*(X - mean)^2

Standard deviation = Sqrt(Variance)

The calculation table is given as below:

X	P(X)	XP(X)	P(X)*(X - mean)^2
0	0.05	0	0.210125
1	0.35	0.35	0.385875
2	0.25	0.5	0.000625
3	0.2	0.6	0.1805
4	0.15	0.6	0.570375
Total	1	2.05	1.3475

Mean = 2.05

Variance = 1.3475

Standard deviation = sqrt(1.3475) = 1.160818677

Standard deviation = 1.161