A gas station sells two types of gasoline: regular and premium. Let X be the amo

Question

A gas station sells two types of gasoline: regular and premium. Let X be the amount (in gallons) of regular sold in a day, and Y = amount (also in gallons) of premium sold in a day. Regular is priced at $4/ gallon and premium at $4.2/ gallon. If E(X) = 2000, E(Y) = 500, Var(X) = 2500, Var(Y) = 10000 and X,Y are independent. Find the expected revenue, E(R), where R = 4X + 4.2Y A gas station sells two types of gasoline: regular and premium. Let X be the amount (in gallons) of regular sold in a day, and Y = amount (also in gallons) of premium sold in a day. Regular is priced at $4/ gallon and premium at $4.2/ gallon. If E(X) = 2000, E(Y) = 500, Var(X) = 2500, Var(Y) = 10000 and X,Y are independent. Find the expected revenue, E(R), where R = 4X + 4.2Y

Explanation / Answer

Here

R = 4X + 4.2 Y

so

E(R) = E(4X + 4.2Y) = E(4X) + E(4.2Y) = 4 E(X) + 4.2 E(Y) (as both are independent)

= 4 * 2000 + 4.2 * 500

= $ 10100

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