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

f(x, y) x y

0.3 50 80

0.2 30 50

0.5 40 60

(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.

x + y f(x + y)

130

80

100

(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. (Round your answer for correlation to two decimal places.)

covariance

correlation

Are x and y positively related, negatively related, or unrelated?

The random variables x and y are ---Select---

• positively related
• negatively related
• 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?

The variance of the sum of x and y is ---Select---

• greater than
• less than
• unrelated

the sum of the variances by two times the covariance, which occurs whenever two random variables are ---Select---

• positively related
• negatively related
• unrelated

.