homework8 - ( ) , ( y f x f y x f Y X XY = Find the p.d.f...

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1 EL 630: Homework 8 Note: Those of you who are seriously interested, should try to solve all these problems in time. 1. X and Y are independent, identically distributed ( i.i.d ) random variables with common p.d.f = - , , 0 , 0 , ) ( otherwise x if e x f x X also = - . , 0 , 0 , ) ( otherwise y if e y f y Y Find the p.d.f of the following random variables (a) Y X + (b) Y X - (c) XY (d) Y X / (e) ) , min( Y X (f) ) , max( Y X (g) . ) , max( ) , min( Y X Y X 2. X and Y are independent r.vs with Geometric p.m.f (29 , , 2 , 1 , 0 , = = = k pq k X P k (29 , , 2 , 1 , 0 , = = = m pq m Y P m and also ( 29 (29 (29 . , m Y P k X P m Y k X P = = = = = Find the p.m.f of (a) Y X + (b) . Y X - 3. X and Y are independent identically distributed normal r.vs with zero mean and common variance , 2 σ i.e., X ), , 0 ( 2 N Y ), , 0 ( 2 N and ). ( )
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Unformatted text preview: ( ) , ( y f x f y x f Y X XY = Find the p.d.f of (a) 2 2 Y X Z + = (b) 2 2 Y X W + = (c) . Y X U-= 4. X and Y are independent and uniform in the interval ( 29 , , a i.e., < = . , , , 1 ) ( otherwise a x a x f X So is ) ( y f Y and ). ( ) ( ) , ( y f x f y x f Y X XY = Find the p.d.f of (a) Y X / (b) Y X Y + (c) . Y X-2 5. X and Y are independent, identically distributed Binomial r.vs with parameters n and p . Show that Y X Z + = is also a Binomial r.v. Find its parameters....
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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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homework8 - ( ) , ( y f x f y x f Y X XY = Find the p.d.f...

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