Question

The revenue (X) from the sales of a compay has an expected value of $6,263, with a standard deviation of $440 while the cost (Y) has an expected value of $4,872, with a standard deviation of $336. The covariance between the revenue and cost is 1,513. What is the variance of the profit (X-Y) of the company

Answer 1

the covariance between the revenue and cost is 1,513. What is the variance of the profit (X-Y) of the company is 303468

Explanation:

Given that;

E(x) = 6263

SD(x) = 440

F(y) = 4872

SD(y) = 336

COVI (x, y) = 1513

Variance x = [ SD(x) ]²

Variance x = [440]² = 193600

Variance y = [ SD(y) ]²

Variance y = [336]² = 112896

Now to get variance of the profit (X-Y) of the company we say;

variance ( x-y ) = variance x + variance y - 2covi(x.y)

we substitute

variance ( x-y ) = 193600 + 112896 - ( 2 × 1513 )

variance ( x-y ) = 306496 - 3026

variance ( x-y ) = 303468

therefore the covariance between the revenue and cost is 1,513. What is the variance of the profit (X-Y) of the company is 303468