Question

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.

c. What is the standard deviation of C?

Answer 1

Standard Deviation =

Standard Deviation = [ (15000*0.50)² + (13000*0.50)² + 2 * 0.50 * 0.50 * 0.90 * 15000 * 13000 ]^1/2

                            = [ 56,250,000 + 42,250,000 + 87,750,000 ]^1/2

                            = [ 186,250,000 ]^1/2

                            = $ 13,647.34 Answer