hw8-solution

# hw8-solution - solution to hw8 6.2(a the pair(X1 X2 has 4...

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solution to hw8 6.2 , (a), the pair ( X 1 ,X 2 ) has 4 possible values: { (1 , 1) , (1 , 0) , (0 , 1) , (0 , 0) } ; Their associated probabilities are: P (1 , 1) = ± 5 2 ± 13 2 = 0 . 1282051; P (1 , 0) = ± 5 1 ¶± 8 1 ± 13 2 2! = 0 . 2564103; P (0 , 1) = ± 5 1 ¶± 8 1 ± 13 2 2! = 0 . 2564103; P (0 , 0) = ± 8 2 ± 13 2 = 0 . 3589744. (b), the triple has 8 possible values: { (1 , 1 , 1) , (1 , 1 , 0) , (1 , 0 , 1) , (1 , 0 , 0) , (0 , 1 , 1) , (0 , 1 , 0) , (0 , 0 , 1) , (0 , 0 , 0) } ; Their associated probabilities are: P (1 , 1 , 1) = ± 5 3 ± 13 3 = 0 . 0349650; P (1 , 1 , 0) = P (1 , 0 , 1) = P (0 , 1 , 1) = ± 8 1 ¶± 5 1 ¶± 4 1 ± 13 3 3! = 0 . 0932401; P (0 , 0 , 1) = P (0 , 1 , 0) = P (1 , 0 , 0) = ± 5 1 ¶± 8 1 ¶± 7 1 ± 13 3 3! = 0 . 1631702; P (0 , 0 , 0) = ± 8 3 ± 13 3 = 0 . 1958042. 6.9 , given joint pdf is f ( x,y ) = 6 7 ( x 2 + xy 2 ), for 0 < x < 1 , 0 < y < 2. (a), veriﬁcation: i), it is positive; 1

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ii), the integral Z 1 0 Z 2 0 6 7 ( x 2 + xy 2 )d y d x = Z 1 0 12 7 x 2 d x + Z 1 0 6 7
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hw8-solution - solution to hw8 6.2(a the pair(X1 X2 has 4...

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