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

In government data, a household consists of all occupants of a dwelling unit, while a family consists of 2 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.
$$\begin{array}{||c|c|c|c|c|c|c|} \hline \text{Number of people}& 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \begin{array}{l} \text { Household } \ \text { probability } \end{array} & 0.25 & 0.32 & 0.17 & 0.15 & 0.07 & 0.03 & 0.01 \\ \hline \begin{array}{l} \text { Family } \ \text { probability } \end{array} & 0 & 0.42 & 0.23 & 0.21 & 0.09 & 0.03 & 0.02 \\ \hline \end{array}$$
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. Find the expected value of each random variable. Explain why this difference makes sense.

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Asma Vang
Household: μ = 2.6 Family: μ = 3.14
We note that the mean number of people in a family (3.14) is greater than the mean number of people in a houschold (2.6), which makes sense as all families have at least 2 people and all households have at least 1 person.