Question

1. For the following probability distribution find the mean, variance, and standard deviation. (complete the chart).

X    p(x) x.p(x) x-μ (x-μ)square root of 2 (x-μ)square root of 2 .p(x)

0 0.125

1 0.375

2 0.375

3 0.125

Mean=

Variance=

Standard deviation=

Answer 1

Solution,

x	p(x)	x * p(x)	x2 * p(x)
0	0.125	0	0
1	0.375	0.375	0.375
2	0.375	0.750	1.50
3	0.125	0.375	1.125
	1.0	1.50	3.0

a) mean = u = x * p(x) = 1.50

b) variance = ² = x² * p(x) - (u)²

variance = ² = 3 - ( 1.5)²

variance = ² = 3 - 2.25

variance = ² = 0.75

c) standard deviation = = x² * p(x) - (u)²

standard deviation = = 3 - ( 1.5)²

standard deviation = = 3 - 2.25

standard deviation = = 0.75

standard deviation = = 0.866