Probability Theory. In a given population of two-earner male-female couples,

male earnings have a mean of $50,000 per year and a standard deviation of $15,000.

Female earnings have a mean of $48,000 per year and a standard deviation of $13,000.

The correlation between male and female earnings for a couple is 0.90. Let C denote the

combined earnings for a randomly selected couple.

a. What is the mean of C?

b. What is the covariance between male and female earnings?

c. What is the standard deviation of C?