homework9 - ( 29 . 1 , Let ). , min( ), , max( Y X Z Y X W...

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1 EL 630: Homework 9 1. The joint p.d.f of the r.vs X and Y is given by Y 1 = . , 0 , , 1 ) , ( otherwise area shaded the in y x f XY -1 1 X -1 Let . Y X Z + = Find and sketch ) ( z F Z and ). ( z f Z 2. X and Y are exponential r.vs with parameters α and β respectively, i.e., ), ( ) ( x U e x f x X - = ). ( ) ( y U e y f y Y - = Further they are given to be independent. Find the p.d.f of (a) Y X 3 + (b) ) 3 , max( Y X (c) ). , 2 min( Y X 3. The joint p.d.f of X and Y is defined as + = . , 0 , 1 , 0 , 0 , 6 ) , ( otherwise y x y x x y x f XY Define . Y X Z - = Find the p.d.f of Z . 4. X and Y are independent uniformly distributed r.vs in
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Unformatted text preview: ( 29 . 1 , Let ). , min( ), , max( Y X Z Y X W = = Find the p.d.f of (a) Z W R-= (b) . Z W S + = 5. X and Y are independent zero meanm Gaussian random variables with common variance . 2 Show that 2 2 Y X Z + = and ) / ( tan 1 X Y-= are also independent r.vs. ( Hint: Compute ). ( ), ( ), , ( f z f z f Z Z Then show that ). ( ) ( ) , ( f z f z f Z Z = )...
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This note was uploaded on 04/24/2011 for the course ECE 6303 taught by Professor Voltz during the Spring '11 term at NYU Poly.

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