231hw6solutionsF11

231hw6solutionsF11 - Will Landau STAT 231 Problem Set 6...

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Unformatted text preview: Will Landau September 20, 2011 STAT 231 Problem Set 6 Solutions Note: for most of the book problems, I borrowed the solution from instructor’s manual. You can tell the difference by the format of the text. Let me know if you would like me to expand on anything. Exercise 6.1 (Devore 5.9) . P ( | X- Y | ≤ 2) = Z Z region III f ( x,y ) dxdy = 1- Z Z I f ( x,y ) dxdy- Z Z II f ( x,y ) dxdy = 1- Z 28 20 Z 30 x +2 ( Kx 2 + Ky 2 ) dydx- Z 30 22 Z x- 2 20 ( Kx 2 + Ky 2 ) dydx = 1- Z 28 20 Kx 2 y + Ky 3 3 30 x +2 dx- Z 30 22 Kx 2 y + Ky 3 3 x- 2 20 dx = 1- Z 28 20 30 Kx 2 + K (30) 3 3- Kx 2 ( x + 2)- K ( x + 2) 3 3 dx- Z 30 22 Kx 2 ( x- 2) + K ( x- 2) 3 3- 20 Kx 2- K (20) 3 3 dx = 1- Z 28 20 26992 K 3- 4 Kx + 26 Kx 2- 4 Kx 3 3 dx- Z 30 22 4 Kx 3 3- 24 Kx 2 + 4 Kx- 8008 K 3 dx = 1- 40576 K- 40576 K = 1- 2 · 40576 · 3 380000 = .3593 1 Exercise 6.2 (Devoer 5.10) . Exercise 6.3 (Devoer 5.12) . 2 Exercise 6.4 (Devoer 5.13) . Exercise 6.5 (Devoer 5.15) . Exercise 6.6 (Devoer 5.18) . 3 Exercise 6.7 (Devoer 5.25) . Exercise 6.8 (Devoer 5.26) . Exercise 6.9 (Devoer 5.27) . 4 Exercise 6.10 (Devoer 5.31) . Exercise 6.11 (Devoer 5.32) ....
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231hw6solutionsF11 - Will Landau STAT 231 Problem Set 6...

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