Question

The U.S. Census Bureau collects demographics concerning the number of people in families per household. Assume the distribution of the number of people per household is shown in the following table:
________________
x P(x)
_______________
2 0.27
3 0.25
4 0.28
5 0.13
6 0.04
7 0.03
a) Calculate the expected number o f people in families per household in the United States.
b) Compute the variance and standard deviation of the number of people in families per household.

Answer 1

(a) mean= E(X)=2*0.27+3*0.25+4*0.28+5*0.13+6*0.04+7*0.03= 3.51

(b) E(X^2) = 2^2*0.27+3^2*0.25+4^2*0.28+5^2*0.13+6^2*0.04+7^2*0.03=13.97

Var(X)=E(X^2) - [E(X)]^2 = 13.97 -3.51^2= 1.6499

Standard deviation =v 1.6499 = 1.284484