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If X and Y are Independent and Identically Distributed (i.i.d.) with: f_{x, y}(x, y)=\frac{1}{9}, \quad x, y \in\{-1,0,1\} Let Z₁ X + Y, Z₂ = X-Y. For each outcome (x, y), compute the outcome (Z₁, Z₂) Are Z₁ and Z₂ independent RVs? Why, or why not? f_{z_{1}, z_{2}}\left(z_{1}, z_{2}\right)=\operatorname{Pr}\left[X+Y=z_{1}, X-Y=z_{2}\right] f_{z_{1}}\left(z_{1}\right)=\Sigma_{z_{2}} f_{z_{1}, z_{2}}\left(z_{1}, z_{2}\right) f_{z_{2}}\left(z_{2}\right)=\sum_{z_{1}} f_{z_{1}, z_{2}}\left(z_{1}, z_{2}\right)

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