Statistics

Adding / Subtracting RVs

Let $X,Y$ be two independent random variables. Then $Var(X\pm Y)=Var(X)+Var(Y)$.

First, show that $Var(X)=\mathbf{E}(x^2)-{\mu }_X^2$ where $x\sim X$. Proof: $$\begin{array}{rl}Var(X)& =\mathbf{E}\left[\right]\end{array}$$

Reference: https://apcentral.collegeboard.org/courses/ap-statistics/classroom-resources/why-variances-add-and-why-it-matters