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Unformatted text preview: X 1 ; :::; X n . So X = f ( Y ) Z = X Y = f ( Y ) Y Y = g ( X; Z ) f. ( X; Z ) are indpendent (see ( d ) ) ( Z; Y ) are dependent: P ( Y = 0 ; Z = 1) = 0 6 = 1 12 & 1 3 = P ( Y = 0) P ( Z = 1) ( X; Y ) are dependent P ( Y = 0 ; X = 3) = 0 6 = 1 12 & 1 2 = P ( Y = 0) P ( X = 3) g. P ( Y = 4 j Z = 1) = P ( Y = 4 ; Z = 1) P ( Z = 1) = 1 = 12 1 = 3 = 1 4 h. E [ Y j Z = 1] = X y y & P ( Y = y j Z = 1) = X y y P ( Y = y; Z = 1) P ( Z = 1) = 1 P ( Z = 1) X y y & P ( Y = y; Z = 1) = = 3 & & 1 & 1 12 + 4 & 1 12 4 & 1 6 = 3 4 2...
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 Spring '10
 MATH187
 Math

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