Points scored by a game participant can be modeled by [math]Z = 3X + 2Y – 5[/math]. [math]X[/math] and [math]Y[/math] are independent random variables with [math]\operatorname{Var} (X) = 3[/math] and [math]\operatorname{Var} (Y) = 4[/math].

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

• 12
• 17
• 38
• 43
• 68

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

Solution: D

Var(Z) = Var(3X + 2Y – 5) = 9Var(X) + 4Var(Y) = 9(3) + 4(4) = 43.

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