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  3. let x ?{1,2} and y ?{3,4} be independent random va

Let X ?{1,2} and Y ?{3,4} be independent random variables with PMF-s: fX(1) = 1 2...

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Basic Math

Let X ?{1,2} and Y ?{3,4} be independent random variables withPMF-s: fX(1) = 1 2 fX(2) = 1 2 fY (3) = 1 3 fY (4) = 2 3 Answer thefollowing questions (a) Write down the joint PMF

(b) Calculate P(X + Y 6 5) and P(Y ?X > 2)

(c) Calculate E(XY ), E(X2Y ), E(?X2+1 Y?2)?

(d) Calculate the Cov(X,Y ), Cov(1?X,3Y + 2) and Var(2X ?Y )(

e*) Calculate Cov(XY,X), Cov(XY,X + Y ) and Var(?X Y)?

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