Question

9. A probability distribution is shown to the right. By hand, find
the mean and standard deviation for the random variable, x, where x represents
the number of bicycles per household in a town of 1000 households. (Use the
easier formula for standard deviation!)

x	P(x)
0	0.125
1	0.428
2	0.256
3	0.108
4	0.083

Mean :___________

Standard Deviation :___________

Answer 1

Solution:

The formula for mean and standard deviation are given as below:

Mean = ∑XP(X)

Variance = ∑(X - mean)*P(X)

Standard deviation = Sqrt[∑(X - mean)*P(X)]

x	P(x)	XP(X)	(X - mean)*P(X)
0	0.125	0	0.318402
1	0.428	0.428	0.152032448
2	0.256	0.512	0.041783296
3	0.108	0.324	0.212891328
4	0.083	0.332	0.479674928
Total	1	1.596	1.204784

Mean = 1.596

Variance = 1.204784

Standard deviation = sqrt(1.204784) = 1.09762653