In government data, a household consists of all occupants of a dwelling unit, while a family consists of two or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States:

Let H = the number of people in a randomly selected U.S. household and F = the number of people in a randomly chosen U.S. family.

a. Here are histograms comparing the probability distributions of H and F. Describe any differences that you observe.

b. Find the expected value of each random variable. Explain why this difference makes sense.

c. The standard deviations of the two random variables are σH = 1.421 and σF = 1.249 . Explain why this difference makes sense.

Transcribed Image Text:

Number of persons 1 2 3 4 5 6 7 Household probability 0.25 0.32 0.17 0.15 0.07 0.03 0.01 Family probability 0.42 0.23 0.21 0.09 0.03 0.02