Question

The 2010 U.S. Census found the chance of a household being a certain size. The data is in the table (" Households by age", 2013).

Household Size 1 2 3 4 5 6 7

Probability 24.7% 35.6% 15.8% 11.7%. 8.3% 3.4% 0.5%

a. Draw a histogram of the probability distribution

b. Find the mean

c. Find the variance

Answer 1

a)

b)

x	P(X=x)	xP(x)	x2P(x)
1	0.2470	0.24700	0.24700
2	0.3560	0.71200	1.42400
3	0.1580	0.47400	1.42200
4	0.1170	0.46800	1.87200
5	0.0830	0.41500	2.07500
6	0.0340	0.20400	1.22400
7	0.0050	0.03500	0.24500
total		2.5550	8.5090
	E(x) =μ=	ΣxP(x) =	2.5550
	E(x2) =	Σx2P(x) =	8.5090
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.980975

from above:

mean =2.555

c)

variance =1.9810