Question

Owner-Occupied Household Size Table P.11 gives the probability function for the random variable \(^{14}\) giving the household size for an owneroccupied housing unit in the US. \({ }^{15}\) (a) Verify that the sum of the probabilities is 1 (up to round-off error). (b) What is the probability that a unit has only one or two people in it? (c) What is the probability that a unit has five or more people in it? \begin{tabular}{lccccccc} \hline\(x\) & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline\(p(x)\) & 0.217 & 0.363 & 0.165 & 0.145 & 0.067 & 0.026 & 0.018 \\ \hline \end{tabular} (d) What is the probability that more than one person lives in a US owner- occupied housing unit?

Short answer

a) The sum of the probability values is 1 when rounded. b) The probability that a unit has one or two people in it is 0.58. c) The probability that a unit has five or more people in it is 0.111. d) The probability that more than one person lives in a US owner-occupied housing unit is 0.784.

Step-by-step solution

Verify the sum of probabilities

Add all the probability values given in the table. These are 0.217, 0.363, 0.165, 0.145, 0.067, 0.026, 0.018.

Calculate the probability of a unit having one or two people

To find the probability that a unit has only one or two people, sum up the probabilities given for one and two people in the table. These are 0.217 and 0.363 respectively.

Calculate the probability of a unit having five or more people

To find the probability that a unit has five or more people, sum up the probabilities given for five, six and seven people in the table. These are 0.067, 0.026 and 0.018 respectively.

Calculate the probability of more than one person living in a unit

To find the probability of more than one person living in a US owner-occupied housing unit, sum up the probabilities of having two, three, four, five, six and seven people living in a unit from the provided table. These probabilities are 0.363, 0.165, 0.145, 0.067, 0.026, 0.018 respectively.