15 6 6 12 1 18 1 3 1 5 2 Y X Y X Y E X E XY E \u03c3 \u03c3 \u03c1 San Jose State University

15 6 6 12 1 18 1 3 1 5 2 y x y x y e x e xy e σ σ

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15 6 6 12 1 18 1 3 1 5 2 ] [ ] [ ] [ , = = × = = Y X Y X Y E X E XY E σ σ ρ
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San Jose State University EE250 (Section 3) Fall 2015 Prof. Kamali Solution to Problem Set #7 1. Problem 5.98 Clearly for , . For , we use the following figure to compute the double integral. 2. Problem 5.106 0 < z 0 ] [ ) ( = = z Z P z F Z 0 > z x y z z z x y + = z x y = x y = z Y X | | ∫ ∫ ∫ ∫ + + + + = = = z z x z x y x z z x y x Z dydx e e dydx e e z Y X P z Z P z F 0 0 ] | [| ] [ ) ( ( ) ( ) + + + + = z z x z x x z z x x Z dx e e e dx e e z F ) ( ) ( 0 ) ( 1 ) ( + + + = z x z z x z z z x z x Z dx e e dx e e dx e e dx e z F 2 2 0 0 2 ) ( z z z z z z Z e e e e e e z F = + = 1 2 1 2 1 ) 1 ( 2 1 1 ) ( 3 2 + + = = > = 0 0 1 ] [ ] [ dz e dz z Z P Z E z
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