d. For a discrete random variable, the sum of the probabilities of its possible

Question

d. For a discrete random variable, the sum of the probabilities of its possible values equals ___________. (terminology)

5.114 Persons per Housing Unit. From the document Amer- ican Housing Survey for the United States, published by the U.S. Census Bureau, we obtained the following frequency distribu- tion 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. Persons 4 Frequency27.9 34.417.0 15.5 6.8 2.3 1.4 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.

Explanation / Answer

a) possible values that Y can take Y={Y| 1,2,3,4,5,6,7}

b) for let random event A for whcih housing unit has exactly 3 person living in it A ={ Y=3}

c) P(Y=3) =household with 3 person/total household =17/(27.9+34.4+17+15.5+6.8+2.3+1.4)=0.1614

which says that 16.14% of total households has exactly 3 person living in it.

d) For a discrete random variable, the sum of the probabilities of its possible values equals 1 .

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