Question
If $X$ and $Y$ are independent random variables with variances $\sigma_{X}^{2}=5$ and $\sigma_{Y}^{2}=3,$ find the variance of the random variable $Z=-2 X+4 Y-3$.
Step 1
If $Z = aX + bY + c$, where $X$ and $Y$ are independent random variables, $a$ and $b$ are constants, and $c$ is a constant, then the variance of $Z$ is given by: \[Var(Z) = a^2Var(X) + b^2Var(Y)\] Show more…
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