Question

Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) x −41 −27 −8 −3 P(X = x) 0.29 0.35 0.21 0.15

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
-41	0.29	-11.89	487.49
-27	0.35	-9.45	255.15
-8	0.21	-1.68	13.44
-3	0.15	-0.45	1.35
Sum	1	-23.47	757.43

Mean = X * P(X)

= -23.47

Variance =

= X 2 * P(X) - 2

= 757.43 - (-23.47)2 = 206.5891

Standard deviation = = 14.3732