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Unformatted text preview: 1 and 0 < y < 1, g ( x,y ) = 0 elsewhere. (b) Find the joint density of ( ZX,ZY ). (c) Find the density of X X + Y . 4. Let X and Y be independent and identically distributed random variables each with a continuous density f ( t ) which is zero if t 6 [0 , 1], and not zero if t (0 , 1). (a) Find an integer n such that lim 1 n P | ( X,Y )- 1 2 , 1 2 | = , where (0 , ) and | ( a,b )-( c,d ) | is the Euclidean distance between these points. Evaluate in terms of f . (b) Find an integer n such that lim 1 n P ( | X-Y | < ) = , where (0 , ). For which f is this minimized?...
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This document was uploaded on 01/25/2012.
- Spring '09