probability distribution

Question

Consider the probability distribution shown below.

x	0	1	2
P(x)	0.25	0.40	0.35

Compute the standard deviation of the distribution. (Round your answer to four decimal places.)

Answer 1

The standard deviation is the square root of the variance.

The variance is the average squared distance from the mean.

First compute the mean: .25*0 +.40*1 + .35*2 = 1.1

The squared distance from the mean for x=0 is (0 - 1.1)^2 which is 1.21

The squared distance from the mean for x=1 is (1 - 1.1)^2 which is 0.01

The squared distance from the mean for x=2 is (2 - 1.1)^2 which is 0.81

The variance is the weighted average of these squared distances:

variance = 0.25 * 1.21 + 0.4 * 0.01 + 0.35 * 0.81 which is 0.59

So the standard deviation is the square root of 0.59 which is 0.7681