160b10_formulas

160b10_formulas - 1 2 Gamma: G ( k, ) , k, > f X...

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Pstat160b Spring 2010 Main formulas Discrete distributions name p X ( k ) = expected value variance Hypergeometric ( N 1 ,N 2 ,n ) N i of type i select n ( N 1 k )( N 2 n - k ) ( N 1 + N 2 n ) 0 k N 1 n - N 2 k n N 1 n N 1 + N 2 Binomial ( n, p ) ( n k ) p k (1 - p ) n - k 1 k n np np (1 - p ) Poisson ( λ ) e - λ λ k k ! k 0 λ λ Geometric ( p ) (1 - p ) k - 1 p k 1 1 p 1 - p p 2 Negative Binomial ( r,p ) ( k - 1 r - 1 ) p r (1 - p ) k - r , k = r,r + 1 , ··· r p r (1 - p ) p 2 Continuous distributions name f X ( x ) = expected value variance Uniform( a,b ) 1 b - a a x b a + b 2 ( b - a ) 2 12 Exponential( λ ) λe - λx x 0 1
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Unformatted text preview: 1 2 Gamma: G ( k, ) , k, > f X ( x ) = k ( k ) x k-1 e-x x k k 2 Normal ( , 2 ) 1 2 e-( x- ) 2 2 2 x R 2 Beta: B ( , ) , , > 1 B ( , ) x -1 (1-x ) -1 x 1 + ( + ) 2 ( + +1) 1...
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This note was uploaded on 01/10/2011 for the course STAT PStat 160b taught by Professor Bonnet during the Spring '10 term at UCSB.

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