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homework11

homework11 - ≤-≥-= 1 1 2 1 2 y x y x y x n n y x f n n...

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1 EL 630: Homework 11 1. X and Y are jointly normal with parameters (29 XY Y X Y X ρ σ μ , , , , 2 2 . Find (a) ] | [ x X Y E = (b) ]. | [ 2 y Y X E = 2. < < < = . , 0 , 1 0 , 6 ) , ( otherwise y x x y x f XY (a) Find ) | ( | y x f Y X and ). | ( | x y f X Y (b) ] | [ Y X E and ]. | [ X Y E 3. (29 - + = . , 0 , 1 | | , 1 | | , ) ( 1 4 1 ) , ( 2 2 otherwise y x y x xy y x f XY Find ] | [ Y X E and ]. | [ X Y E 4. X , Y are independent identically distributed exponential random variables with parameter . λ Let . ) , 2 max( Y X Y Z = Find ). ( z f Z 5. The joint density function of X and Y is given to be ( Note 1 1 , 1 1 < < - < < - y x )
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Unformatted text preview: ≤-≥--=-. , , 1 1 , ) ( 2 ) 1 ( ) , ( 2 y x y x y x n n y x f n n XY Show that the probability distribution function of Y X Z-= is given by < ≤ ---≥ =-. , , 2 , 1 1 2 2 ) 1 ( , 2 , 1 ) ( 1 otherwise z z n z n n n z z F n n n Z...
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