3. (18/222, Expected Value and Variance) The Philippine Housing Survey reported the following data on the number of bedrooms in owner-occupied and renter-occupied houses in central cities of the country. E(x) = Var (x) = 6x = a. Define a random variable x = number of bedrooms in renter-occupied houses and develop a probability distribution for the random variable. Let x = 4 represent 4 or more bedrooms. Show tabular computation/solution. Compute the expected value, variance, and standard deviation for the number of bedrooms in renter-occupied houses E(y) = Bedrooms Var (y) = 0 1 2 3 4 or more Ov= Number of Houses (1,000s) Owner-Occupied 23 541 3,832 8,690 3,783 16,869 Renter-Occupied 547 b. Define a random variable y = number of bedrooms in owner-occupied houses and develop a probability distribution for the random variable. Let y = 4 represent 4 or more bedrooms. Show tabular computation/solution. Compute the expected value, variance, and standard deviation for the number of bedrooms in owner-occupied houses. 5,012 6,100 2,644 557 14,860 c. What observations can you make from a comparison of the number of bedrooms in renter-occupied versus owner-occupied homes? 3

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3. (18/222, Expected Value and Variance) The Philippine Housing Survey reported the following data on the
number of bedrooms in owner-occupied and renter-occupied houses in central cities of the country.
E(x) =
Var (x) =
6x =
Bedrooms
a. Define a random variable x = number of bedrooms in renter-occupied houses and develop a
probability distribution for the random variable. Let x = 4 represent 4 or more bedrooms. Show
tabular computation/solution. Compute the expected value, variance, and standard deviation for the
number of bedrooms in renter-occupied houses
E(y) =
0
1
2
3
4 or more
Var (y) =
Number of Houses (1,000s)
Owner-Occupied
23
541
3,832
8,690
3,783
16,869
Renter-Occupied
547
5,012
6,100
2,644
557
14,860
b. Define a random variable y = number of bedrooms in owner-occupied houses and develop a
probability distribution for the random variable. Let y = 4 represent 4 or more bedrooms. Show
tabular computation/solution. Compute the expected value, variance, and standard deviation for the
number of bedrooms in owner-occupied houses.
c. What observations can you make from a comparison of the number of bedrooms in renter-occupied
versus owner-occupied homes?
3
Transcribed Image Text:3. (18/222, Expected Value and Variance) The Philippine Housing Survey reported the following data on the number of bedrooms in owner-occupied and renter-occupied houses in central cities of the country. E(x) = Var (x) = 6x = Bedrooms a. Define a random variable x = number of bedrooms in renter-occupied houses and develop a probability distribution for the random variable. Let x = 4 represent 4 or more bedrooms. Show tabular computation/solution. Compute the expected value, variance, and standard deviation for the number of bedrooms in renter-occupied houses E(y) = 0 1 2 3 4 or more Var (y) = Number of Houses (1,000s) Owner-Occupied 23 541 3,832 8,690 3,783 16,869 Renter-Occupied 547 5,012 6,100 2,644 557 14,860 b. Define a random variable y = number of bedrooms in owner-occupied houses and develop a probability distribution for the random variable. Let y = 4 represent 4 or more bedrooms. Show tabular computation/solution. Compute the expected value, variance, and standard deviation for the number of bedrooms in owner-occupied houses. c. What observations can you make from a comparison of the number of bedrooms in renter-occupied versus owner-occupied homes? 3
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