Question: 25. Given below is a bivariate distribution for the random variables x and y. f (x, y) x y .2 50 80 .5 30 50

25. Given below is a bivariate distribution for the random variables x and y.

f (x, y) x y

.2 50 80

.5 30 50

.3 40 60

a. Compute the expected value and the variance for x and y.

b. Develop a probability distribution for x + y.

c. Using the result of part (b), compute E(x + y) and Var (x + y).

d. Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?

e. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?

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