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2. Suppose XBinomial(1,0.4) and YBinomial(2,0.4), respectively. Additionally, we assume P(X=1,Y =2)=0 and X and Y are uncorrelated. [5] (a) Find the joint probability function of X and Y. (You may write it as a table.) [3] (b) Find P(XY). [2] (c) Is X independent of Y ? Justify your reasoning..

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2. Suppose XBinomial(1,0.4) and YBinomial(2,0.4), respectively. Additionally, we assume P(X=1,Y =2)=0 and X and Y are uncorrelated. [5] (a) Find the joint probability function of X and Y. (You may write it as a table.) [3] (b) Find P(XY). [2] (c) Is X independent of Y ? Justify your reasoning.

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