Revision as of 13:50, 6 May 2023 by Admin (Created page with "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>\operatorna...")
ABy Admin
May 06'23
Exercise
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.
ABy Admin
May 06'23
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.