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	−32	−20	−10	−5
P(X = x)	0.46	0.24	0.18	0.12

Answer 1

Solution:

We have to find:  the mean, the variance, and the standard deviation of the following discrete probability distribution.

x	−32	−20	−10	−5
P(X = x)	0.46	0.24	0.18	0.12

Formula:

Mean:

Variance:

where

standard deviation:

Thus we need to make following table:

x	P(X = x)	x*P(x)	x 2 *P(x)
-32	0.46	-14.7200	471.0400
-20	0.24	-4.8000	96.0000
-10	0.18	-1.8000	18.0000
-5	0.12	-0.6000	3.0000

Thus

Mean:

Variance:

where

thus

and

standard deviation: