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# tutorial10 - U = XY and V = X/Y . (b) Find the marginal...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 PROBABILITY AND STATISTICS I EXAMPLE CLASS 10 EX.1 Let X and Y be random variables with joint pdf f ( x,y ) = ( 2 xe - y y 2 , if 0 < x < y < 0 , otherwise . Let W = Y - X, Z = Y + X . Find the joint pdf of W and Z . 1

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EX.2 Suppose X and Y have joint density function f ( x,y ) = ( 1 x 2 y 2 , if x > 1 ,y > 1 0 , otherwise . (a) Find the joint density function of

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Unformatted text preview: U = XY and V = X/Y . (b) Find the marginal pdfs of U and V . 2 EX.3 Suppose X , Y and Z are independently and identically distributed as Exp (1). Derive the joint distribution of U = X + Y , V = X + Z and W = Y + Z . 3 EX.4 Suppose X,Y iid ∼ U (0 , 1). Find the pdf of Z = X + Y . 4...
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## This note was uploaded on 01/16/2012 for the course STAT 1301 taught by Professor Smslee during the Fall '08 term at HKU.

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tutorial10 - U = XY and V = X/Y . (b) Find the marginal...

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