Unformatted text preview: Î¼ , prove that X + Y has a Poisson distribution with parameter Î» + Î¼ . 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 â‰¤ Â·Â·Â· â‰¤ U nn . (a) Prove that nU n 1 converges in distribution as n â†’ âˆž and identify the limit. (b) Prove that nU n 2 converges in distribution as n â†’ âˆž and identify the limit....
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 Spring '11
 NA
 Normal Distribution, Poisson Distribution, Probability, Probability theory, Let Xi, Unn

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