Question
Given below is a bivariate distribution for the random variables x and y. f(x, y) x...
Given below is a bivariate distribution for the random variables x and y.
| f(x, y) | x | y |
| 0.1 | 90 | 90 |
| 0.5 | 30 | 40 |
| 0.4 | 50 | 70 |
a. Compute the expected value and the variance for x and y.
| E(x) | = | |
| E(y) | = | |
| Var(x) | = | |
| Var(y) | = |
b. Develop a probability distribution for x + y. Round your answers to one decimal place.
| x + y | f(x + y) |
| 180 | |
| 70 | |
| 120 |
c. Using the result of part (b), compute E(x + y) and Var(x + y).
| E(x + y) | = | |
| Var(x + y) | = |
d. Compute the covariance and correlation for x and y. If required, round your answers to two decimal places.
| Covariance | = | |
| Correlation | = |
The random variables x and y are - Select your answer -positively relatednegatively relatedunrelatedItem 12 .
e. The variance of the sum of x and y is - Select your answer -biggersmallerthe sameItem 13 than the sum of the individual variances.
By how much?
- Select your answer -Var(x+y) is less than Var(x) + Var(y) by twice the covariance Var(x+y) equals Var(x) + Var(y) Var(x+y) is greater than Var(x) + Var(y) by twice the covariance
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