Consider two random variables X and Y with the range Rxy = {(i, j) € Z² | i,j> 0, |i – j| < 1}, and joint PMF given by 1 Pxy(i, j) = for (i, j) € Rxy- 6 - 2min(ij) * 1. Pictorially show Rxy in the ry plane. 2. Find the marginal PMFS Px(i), Py(j). 3. Find P(X = Y |X < 2). 4. Find P(1 < X² +Y² < 5). 5. Find P(X = Y). 6. Find E[X |Y = 2]. 7. Find Var(X |Y = 2).

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