NotesOct6 - The Poisson random variable is the limiting...

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The Poisson random variable is the limiting case of the Binomial random variable as: n → ∞ ; p 0; np λ > 0. Notation : X Poiss( λ ). p X ( k ) = e - λ λ k k ! , k = 0 , 1 , 2 ,....
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Reproducing property of Poisson random variables Let X 1 ,X 2 ,...,X n be independent Poisson ran- dom variables with parameters λ 1 2 ,...,λ n . Then the sum Y = X 1 + X 2 + ... + X n has the Poisson distribution with parameter λ 1 + λ 2 + ... + λ n .
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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 b - a if a x b 0 otherwise. Notation : X U( a,b ).
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offers flexible shapes of a density of a bounded interval. A random variable X has the Beta distribution on [0 , 1] with parameters α > 0 and β > 0 if it has the density f X ( x ) = ( 1 B ( α,β ) x α - 1 (1 - x ) β - 1 if 0 < x < 1 0 otherwise. Notation
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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.

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NotesOct6 - The Poisson random variable is the limiting...

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