Persons per Housing Unit. From the document American Housing Survey for the United States, published by the U.S. Census Bureau, we obtained the following frequency distribution for the number of persons per occupied housing unit, where we have used “7” in place of “7 or more.” Frequencies are in millions of housing units.

 For a randomly selected housing unit, let Y denote the number of persons living in that unit.

a. Identify the possible values of the random variable Y .
b. Use random-variable notation to represent the event that a housing unit has exactly three persons living in it.
c. Determine P(Y = 3); interpret in terms of percentages.
d. Determine the probability distribution of Y .
e. Construct a probability histogram for Y .

Persons 2 3 4 5 6 7 Frequency 27.9 34.4 17.0 15.5 6.8 2.3 1.4