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Question 4: [10 Marks: 3, 3, 2, 2] X and Y are discrete random variables with joint distribution given below Y=-1 Y = 0 Y = 1

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Variables with Solution Total x and discrete random Joint distribution y=-1 14 14 O 1 6 314 Total 2/4 1 Deleamine conditionalE(YIX=1) = { Y P (41 X = 1) = (-1) Tot of it E(Ylx=1) 63 Determine Conditional for each value ofy expectation E(XlY=Y) E (X=-Conditional Prob. distribution of yly=-) 0 P (4 141) E (X11=1) Zap(x/y=1 lxotox) EX/Y=-1) Tofind E ( Xly-o) conditional ProbaEctly=0) {X PCX ly=0) IX 2 2 [(x/4.0) 2 To find Exly=1) conditional probability or P(x = 1/4-1) P(x = 1, y=1) Pry=1) 1/4 P(x=We law of it erated know that from expectation. •ECE (x14 g(y) = E(x/y=Y) ELE (+14) [ (g(y) E (4) P(Y) -EE(X=y) PCY) E LE (X/CAT ed To obtain marginal distribution of you Total YO O 14 44 3/4 Total 2/4 1 Marginal distribution of X 1 Х P(x) 314 e F(x)

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