4. Suppose X, Y are two discrete RV's with joint p.m.f. given by the table: XY...

 

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4. Suppose X, Y are two discrete RV's with joint p.m.f. given by the table: XY 1 1/2 0 1/12 1/8 1/8 1/12 2 3 1 0 1/12 1/9 1/9 6 1/12 1/12 0 1/9 (a) Calculate the marginal p.m.f. of X and of Y. (b) Calculate P(X + Y < 3). (c) Are X and Y independent? 4. Suppose X, Y are two discrete RV's with joint p.m.f. given by the table: XY 1 1/2 0 1/12 1/8 1/8 1/12 2 3 1 0 1/12 1/9 1/9 6 1/12 1/12 0 1/9 (a) Calculate the marginal p.m.f. of X and of Y. (b) Calculate P(X + Y < 3). (c) Are X and Y independent?