The following data have been collected on the number of times that owner-occupied and renter-occupied units had a water supply stoppage lasting or more hours over a -month period. Number of Units (1,000s) Number of Times Owner Occupied Renter Occupied 0 548 23 1 5,012 541 2 6,110 3,734 3 2,544 8,660 4 times or more 557 3,784 Do not round intermediate calculations. Round your answers to two decimal places. a. Define a random variable number of times that owner-occupied units had a water supply stoppage lasting or more hours in the past months and develop a probability distribution for the random variable. (Let represent or more times.) x f(x) 0 1 2 3 4 Total b. Compute the expected value and variance for x. E(x) Var(x) c. Define a random variable number of times that renter-occupied units had a water supply stoppage lasting or more hours in the past months and develop a probability distribution for the random variable. (Let represent or more times.) y f(y) 0 1 2 3 4 Total d. Compute the expected value and variance for y. E(y) Var(y)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The following data have been collected on the number of times that owner-occupied and renter-occupied units had a water supply stoppage lasting or more hours over a -month period.
| Number of Units (1,000s) | ||||
| Number of Times | Owner Occupied | Renter Occupied | ||
| 0 | 548 | 23 | ||
| 1 | 5,012 | 541 | ||
| 2 | 6,110 | 3,734 | ||
| 3 | 2,544 | 8,660 | ||
| 4 times or more | 557 | 3,784 |
Do not round intermediate calculations. Round your answers to two decimal places.
a. Define a random variable number of times that owner-occupied units had a water supply stoppage lasting or more hours in the past months and develop a probability distribution for the random variable. (Let represent or more times.)
| x | f(x) |
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| Total |
b. Compute the expected value and variance for x.
| E(x) | |
| Var(x) |
c. Define a random variable number of times that renter-occupied units had a water supply stoppage lasting or more hours in the past months and develop a probability distribution for the random variable. (Let represent or more times.)
| y | f(y) |
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| Total |
d. Compute the expected value and variance for y.
| E(y) | |
| Var(y) |
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