solution11

# solution11 - EL630 Homework11 Solutions 1(a The joint p.d.f...

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Unformatted text preview: EL630: Homework11 Solutions 1. (a) The joint p.d.f. of X and Y is - +------- = 2 2 2 2 2 ) ( ) ( ) ( 2 ) ( ) 1 ( 2 1 1 2 1 ) , ( y y y x y x xy x x xy y y x x xy y x XY e y x f σ μ σ σ μ μ ρ σ μ ρ ρ σ σ π . Therefore, since ) ( ) , ( ) ( x f y x f x y f X XY X Y = , we have 2 2 2 2 2 2 2 2 ) ( ) ( ) ( ) ( 2 ) ( ) 1 ( 2 1 2 1 1 2 1 ) ( x x y y y x y x xy x x xy x x y y x x xy y x X Y e e x y f σ μ σ μ σ σ μ μ ρ σ μ ρ π σ ρ σ σ π-- - +------- = - +------- = 2 2 2 2 2 2 ) ( ) ( ) ( 2 ) ( ) 1 ( 2 1 1 2 1 ) ( x x xy y x y x xy y y xy x y x y xy y X Y e x y f σ μ ρ σ σ μ μ ρ σ μ ρ ρ σ π This can be written in the form - + + - +---- = 2 2 2 2 ) ( ) ( 2 ) 1 ( 2 1 1 2 1 ) ( x x y xy y x x y xy y xy y x y x y xy y X Y e x y f σ μ σ ρ μ σ μ σ ρ μ ρ σ ρ σ...
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solution11 - EL630 Homework11 Solutions 1(a The joint p.d.f...

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