Profit for a new product is given by [math]Z = 3X-Y-5[/math]. [math]X[/math] and [math]Y[/math] are independent random variables with [math]\operatorname{Var}(X) = 1 [/math] and [math]\operatorname{Var}(Y) = 2[/math].

Calculate [math]\operatorname{Var}(Z)[/math]

• 1
• 5
• 7
• 11
• 16

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: D

Note that due to the independence of X and Y Var(Z) = Var(3X − Y − 5) = Var(3X) + Var(Y) = 32 Var(X) + Var(Y) = 9(1) + 2 = 11 .

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.