calculation questions

Question 1

Derive the expected aggregate daily revenue from the sales of these three types of pizzas. (Question 5)

Answer 1

E(5X1 + 7X2 + 9X3)
=5E(X1) + 7E(X2) + 9E(X3)
=5(25) + 7(57) + 9(40)
=125 + 399 + 360
=£884

Question 2

Derive the standard deviation of the aggregate dailly revenue from the sales of these three types of pizza

Answer 2

Var(Rtotal)
=Var(X1 x 5 + X2 x 7 + X3 + 9)
=5sq x Var(X1) + 7sq x Var(X2) + 9sq x Var(X3)
=25 x 75 + 49 x 148 + 120
σsq=£18847

Standard deviation of the aggregate daily revenue (σtotal) is:
σtotal = Var(Rtotal) =18847
squareroot of σ = 137.28