Question

Assume that the following table is the probability distribution of X:
X 0 1 2 3   
P(X) 0.10 0.30 0.40 0.20

What are the “expected value” and “standard deviation” of X? Show your work.

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
0	0.1	0	0
1	0.3	0.3	0.3
2	0.4	0.8	1.6
3	0.2	0.6	1.8
		0	0
Sum	1	1.7	3.7

Mean = X * P(X)

= 1.7

Standard deviation =

=X 2 * P(X) - 2

=  3.7 - (1.7)2  = 0.81

Standard deviation = = 0.9