# lec30 - x,y = 60 x 2 y x> y> x y ≤ 1 otherwise(a Find...

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36-225 – Handout for Lecture # 30 November 3, 2010 1. Consider the following joint p.d.f: P XY ( x,y ) = e - 2 λ λ x + y x ! y ! x = 0 , 1 , 2 , 3 ... y = 0 , 1 , 2 , 3 ... λ > 0 (a) Find and recognize the marginal distributions P X ( x ) and P Y ( y ). (b) Are X and Y independent random variables? 2. Suppose that the joint pdf of ( X,Y ) is given by: f XY ( x,y ) = 1 80 ( xy + 1) 0 < x < 4 , 0 < y < 4 0 otherwise Find the marginal distribution of X , f X ( x ). 3. Suppose that the joint pdf of ( X,Y ) is given by: f XY
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Unformatted text preview: ( x,y ) = 60 x 2 y x > , y > , x + y ≤ 1 otherwise (a) Find and recognize the marginal distributions f X ( x ) and f Y ( y ). (b) Are X and Y independent random variables? 4. Suppose X and Y are independent random variables with f X ( x ) = b 3 x 2 < x < 1 otherwise f Y ( y ) = b 3 y 2 < y < 1 otherwise Find P ( Y < X 2 )....
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