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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>. | 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> | |||
<ul class="mw-excansopts"> | <ul class="mw-excansopts"> | ||
<li> | <li>1</li> | ||
<li> | <li>5</li> | ||
<li> | <li>7</li> | ||
<li> | <li>11</li> | ||
<li> | <li>16</li> | ||
</ul> | </ul> | ||
{{soacopyright | 2023}} | {{soacopyright | 2023}} | ||
Latest revision as of 15:08, 6 May 2023
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]
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Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.