Question

Find the mean, variance and standard deviation for the probability distribution given below:

X	-2	3	12	9
P(X)	0.556	0.109	0.206	0.129

Round to three decimal places.

A. Mean =

B. Variance =

C. Standard Deviation =

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
-2	0.556	-1.112	2.224
3	0.109	0.327	0.981
12	0.206	2.472	29.664
9	0.129	1.161	10.449
Sum	1	2.848	43.318

Mean = X * P(X)

= 2.848

Variance

= X 2 * P(X) - 2

= 43.318 - (2.848)2 = 35.2069

Standard deviation = = 5.934