The following data has been collected 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 Times | Number of Units (1,000s) | |
|---|---|---|
| Owner Occupied | Renter Occupied | |
| 0 | 439 | 394 |
| 1 | 1,200 | 760 |
| 2 | 249 | 221 |
| 3 | 96 | 92 |
| 4 times or more | 120 | 111 |
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. Round your answers to four decimal places.)
| x | f(x) | xf(x) | x − ???? | (x − ????)2 | (x − ????)2f(x) |
|---|---|---|---|---|---|
| 0 | |||||
| 1 | |||||
| 2 | |||||
| 3 | |||||
| 4 |
b) Compute the expected value and variance for x. (Round your answers to four decimal places.)
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. Round your answers to four decimal places.)
| y | f(y) | yf(y) | y − ???? | (y − ????)2 | (y − ????)2f(y) |
|---|---|---|---|---|---|
| 0 | |||||
| 1 | |||||
| 2 | |||||
| 3 | |||||
| 4 |
d) Compute the expected value and variance for y. (Round your answers to four decimal places.
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 expected number of times that owner-occupied units have a water supply stoppage lasting 6 or more hours in the past 3 months is ---Select--- less than, greater than, or equal to the expected value for renter-occupied units. The variability for owner-occupied units is ---Select--- less than, greater than, or equal to the variability for renter-occupied units.