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wackerly statsitcial inference 5.91

# wackerly statsitcial inference 5.91 - 2 dy 1 dy 2 Ans f 1(y...

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Question: 5.91 statistical inference ( Wackerly) Let Y1 and Y2 have the joint probability density function given by: f(y1,y2) = {K(1-2y2), 0 ≤y ≤1, 0 ≤ 1 = { 0, elsewhere Show that Cov(Y1, Y2) = 0. Does this surprise you that Cov(Y1, Y2) is zero? Why? Solve: Cov(Y1, Y2) = E ( Y1, Y2) – E(Y1)E(y2) We need: -E ( Y1, Y2) = ∫ - ∫- y 1 .y 2 .f(y1, y2) dy 1 dy 2 -E(Y1)= ∫ - ∫- y 1 .f(y 1 , y2 ) dy 1 dy 2 -E(y2)= ∫ - ∫- y 2 .f(y

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Unformatted text preview: 2 ) dy 1 dy 2 Ans: f 1 (y 1 ) =âˆ« 1 4y1y 2 dy 2 = 2y 1 fy 2 (y 2 ) =âˆ« 1 4y1y 2 dy 1 =2y 2 E(y1) = 2/3 E(Y2) = 2/3 E(Y1, Y2) = 4/9 Therefore, Cov(Y1, Y2) = E ( Y1, Y2) â€“ E(Y1)E(y2) Cov(Y1, Y2) = 4/9 â€“ (2/3)(2/3) = Note: As the variables are independent the variables are uncorrelated. f(y 1 , y 2 ) = f(y 1 )f(y 2 ) â€¦â€¦â€¦. If independent 4y 1 y 2 = (2.y 1 ) (2.y 2 ) â€¦â€¦â€¦â€¦â€¦â€¦â€¦. . true....
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wackerly statsitcial inference 5.91 - 2 dy 1 dy 2 Ans f 1(y...

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