# HW8-sol - NTHU MATH 2810, 2011 Solution to Homework 8 2....

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39 5 12 13 4 5 ) 1 , 1 ( 39 10 12 13 5 8 ) 1 , 0 ( 39 14 12 13 7 8 ) 0 , 0 ( ) ( . 2 P P P a 143 5 11 12 13 3 4 5 ) 1 , 1 , 1 ( 429 40 13 4 5 8 ) 0 , 1 , 1 ( ) 1 , 0 , 1 ( ) 1 , 1 , 0 ( 70 5 7 8 ) 0 , 0 , 1 ( ) 0 , 1 , 0 ( ) 1 , 0 , 0 ( 28 6 7 8 ) 0 , 0 , 0 ( ) ( P P P P P P P P b 10 1 3 4 5 1 2 3 ) 0 , 4 ( ) 5 , 4 ( 10 2 2 3 4 5 1 2 2 3 2 ) 1 , 3 ( (3,5) , (3,4) 10 2 2 3 4 5 1 2 2 3 2 ) 2 , 2 ( (2,5) , (2,4) 10 1 3 4 5 1 2 3 ) 1 , 2 ( ) 3 , 2 ( 10 2 2 3 4 5 1 2 3 2 2 ) 3 , 1 ( (1,5) , (1,4) 10 1 3 4 5 1 3 2 ) 2 , 1 ( (1,3) 10 1 4 5 1 2 ) 1 , 1 ( ) 2 , 1 ( ) , ( : : : ) , ( . 6 2 1 2 1 P P P P P P P N N P N N b a (a,b) (1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) (3,4) (3,5) (4,5) (N 1 ,N 2 ) (1,1) (1,2) (1,3) (1,3) (2,1) (2,2) (2,2) (3,1) (3,1) (4,0) P(N 1 ,N 2 ) 10 1 1 1 1 1 1 1 1 1 1 Hence the joint pmf of (N 1 ,N 2 ): (N 1 ,N 2 ) (1,1) (1,2) (1,3) (2,1) (2,2) (3,1) (4,0) P(N 1 ,N 2 ) 1 1 2 1 2 2 1 NTHU MATH 2810, 2011 Solution to Homework 8 Jointly made by 趙±² 劉³´ 黃µ¶ 助·

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8 1 1 3 4 1 ) ( ) ( . 8 0 3 0 2 2 c dy e y c dxdy e x y c a y y y y y e y dx e x y y f b y y y y Y 0 6 1 ) ( 8 1 ) ( ) ( 3 2 2 x x e e x e ye e y dy e x y x f x b y x y y y y y b x y X |) | 1 ( 4 1 2 2 8 1 ) ( 8 1 ) ( | | | | 2 2 | | 2 2 lim 1 0 2 0 1 0 2 1 0 2 0 2 2 1 6 7 7 6 2 7 6 2 7 6 ) , ( 1 0 , 2 0 ) 2 ( 7 6 ) , ( ) ( . 9 dx x x dydx xy x y x f x y xy x y x f a 1 0 ) 2 ( 7 6 ) 2 ( 7 6 ) ( ) ( 2 2 0 2 x x x dy xy x x f b X 1 0 3 3 1 00 2 56 15 ) 16 1 4 1 ( 7 6 4 1 7 6 ) 2 ( 7 6 ) ( dx x x dydx xy x Y X P c x
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## This note was uploaded on 02/12/2012 for the course MATH 2810 taught by Professor Shao-weicheng during the Fall '11 term at National Tsing Hua University, China.

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HW8-sol - NTHU MATH 2810, 2011 Solution to Homework 8 2....

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