Homework Answers
The variance of Z is given by:
![\begin{align*} \boldsymbol{\sigma^2_Z} &= Var(Z) \\ &= Var(3X-Y-5) \\ &= Var(3X-Y) \\ &\left[\text{Using: Var(variable + constant) = Var(variable)} \right ] \\ &= Var(3X) +Var(Y) \\ &\text{[Since, X and Y are independent]} \\ &[\text{Using: For independent random variables A and B:} \\ &\text{Var(A - B) =Var(A) + Var(B)}] \\ &= 3^2*Var(X) + Var(Y) \\ &[\text{Using: Var(constant*variable) = constant}^2\text{*Var(variable)} ] \\ &= 9\sigma^2_X + \sigma^2_Y \\ &= 9*1^2 + \left(\sqrt{2} \right )^2 \\ &= 9*1 + 2 \\ &= 9+2 \\ &= \bf 11 \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ANSWER] \end{align*}](http://img.homeworklib.com/questions/583ace10-0e81-11eb-8d1c-4f8064800342.png?x-oss-process=image/resize,w_560)
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