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Unformatted text preview: , prove that X + Y has a Poisson distribution with parameter + . 4. Let U 1 ,...,U n be independent and uniformly distributed on (0 , 1). Let U n 1 ,...,U nn be the order statistics of U 1 ,...,U n , that is an arrangement of U 1 ,...,U n in increasing order. Thus U n 1 U nn . (a) Prove that nU n 1 converges in distribution as n and identify the limit. (b) Prove that nU n 2 converges in distribution as n and identify the limit....
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This note was uploaded on 06/19/2011 for the course MATH 680 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.
- Spring '11