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Unformatted text preview: . A success = drawing a type A object . Probability mass function: p X ( k ) = N k M nk N + M n , max( nM, 0) k min( n,N ) . The Poisson random variable is the limiting case of the Binomial random variable as: n ; p 0; np > 0. Notation : X Poiss( ). p X ( k ) = e k k ! , k = 0 , 1 , 2 ,.... Reproducing property of Poisson random variables Let X 1 ,X 2 ,...,X n be independent Poisson random variables with parameters 1 , 2 ,..., n . Then the sum Y = X 1 + X 2 + ... + X n has the Poisson distribution with parameter 1 + 2 + ... + n . Review of the important continuous random variables 1. Continuous models on a bounded interval The Uniform random variable takes values in a bounded interval ( a,b ), and has a constant density f X ( x ) = ( 1 ba if a x b otherwise. Notation : X U( a,b )....
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This note was uploaded on 12/03/2010 for the course OR&IE 3500 taught by Professor Samorodnitsky during the Fall '10 term at Cornell University (Engineering School).
 Fall '10
 SAMORODNITSKY

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