Question

he American Housing Survey reported the following data on the number of times that owner-occupied and renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months.

	Number of Houses (1000s)
Number of Times	Owner Occupied		Renter Occupied
0	549		23
1	5,012		542
2	6,100		3,734
3	2,544		8,690
4 times or more	558		3,783

Do not round intermediate calculations. Round your answers to two decimal places.

a. Define a random variable x = number of times that owner-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let x = 4 represent 4 or more times.)

x	f(x)
0
1
2
3
4
Total

b. Compute the expected value and variance for x.

	Total
E(x)
Var(x)

c. Define a random variable y = number of times that renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let y = 4 represent 4 or more times.)

y	f(y)
0
1
2
3
4
Total

d. Compute the expected value and variance for y.

	Total
E(y)
Var(y)

e. What observations can you make from a comparison of the number of water supply stoppages reported by owner-occupied units versus renter-occupied units?

The number of times of water supply stoppages in owner-occupied houses is SelectgreaterlessItem 17 than in renter-occupied houses, and the variability in the number of times is SelectgreaterlessItem 18 for the owner-occupied houses

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Solution

Answer 1

(a)

Following table shows the probability distribution:

X	Frequency, f	P(X=x), f/14763
0	549	0.04
1	5012	0.34
2	6100	0.41
3	2544	0.17
4	558	0.04
Total	14763	1

(b)

Following table shows the calculations:

X	P(X=x)	xP(X=x)	x^2*P(X=x)
0	0.04	0	0
1	0.34	0.34	0.34
2	0.41	0.82	1.64
3	0.17	0.51	1.53
4	0.04	0.16	0.64
Total		1.83	4.15

So,

(c)

Following table shows the calculations

Y	Frequency	P(Y=y), f /16772
0	23	0.001
1	542	0.032
2	3734	0.223
3	8690	0.518
4	3783	0.226
Total	16772	1

(d)

Y	P(Y=y)	yP(Y=y)	y^2*P(Y=y)
0	0.001	0	0
1	0.032	0.032	0.032
2	0.223	0.446	0.892
3	0.518	1.554	4.662
4	0.226	0.904	3.616
Total		2.936	9.202

So,