Question

The revenue (X) from the sales of a compay has an expected value of $7,403, with a standard deviation of $551 while the cost (Y) has an expected value of $4,566, with a standard deviation of $348. The covariance between the revenue and cost is 1,434. What is the variance of the profit (X-Y) of the company?

Hint: Answer should be accurate to 0 decimal place, i.e., an integer.

Answer 1

X : sales/revenue

Y : Cost

Given,

The revenue (X) from the sales of a company has an expected value of $7,403, with a standard deviation of $551 i.e

E(X) = $7403

Standard deviation of X = $551

Variance of X = 551*551 = 303601

Var(X) = 303601

the cost (Y) has an expected value of $4,566, with a standard deviation of $348

E(Y) = $4566

standard deviation of Y =  $348

Variance of Y : Var(Y) = 348 x 348 = 121104

Covariance between the revenue and cost is 1,434

Cov(X,Y) = 1434

Z : X-Y = Sales - Cost

variance of the profit (X-Y) of the company = Var(Z) = Var(X-Y)

Var(Z) = Var(X-Y) = Var(X) + Var(Y) -2Cov(X,Y) = 303601 + 121104 - 2*1434= 421837

Variance of the profit (X-Y) of the company = 421837