some_distributions - a ) 2 12 Gamma( n , ) f ( x ) = n x...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Results for Some Fundamental Probability Distributions Discrete Probability Mass Function Mean Variance Distribution of X E( X ) Var( X ) Binomial( n,p ) p ( x ) = ( n x ) p x (1 - p ) n - x , x = 0 , 1 ,...,n np np (1 - p ) Bernoulli( p ) p ( x ) = p x (1 - p ) 1 - x , x = 0 , 1 p p (1 - p ) HG( N,r,n ) [*] p ( x ) = ( r x )( N - r n - x ) ( N n ) , x = max { 0 ,n - N + r } ,..., min { n,r } nr N nr ( N - r )( N - n ) N 2 ( N - 1) Poisson( λ ) p ( x ) = e - λ λ x x ! , x = 0 , 1 ,... λ λ NB( k,p ) [**] p ( x ) = ( x - 1 k - 1 ) p k (1 - p ) x - k , x = k,k + 1 ,... k p k (1 - p ) p 2 Geometric( p ) p ( x ) = (1 - p ) x - 1 p , x = 1 , 2 ,... 1 p 1 - p p 2 Continuous Probability Density Function Mean Variance Distribution of X E( X ) Var( X ) Uniform( a,b ) f ( x ) = 1 b - a , a < x < b a + b 2 ( b -
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a ) 2 12 Gamma( n , ) f ( x ) = n x n-1 e-x ( n-1)! , x &gt; n n 2 Exponential( ) f ( x ) = e-x , x &gt; 1 1 2 Normal( , 2 ) f ( x ) = 1 2 e-( x- ) 2 2 2 ,- &lt; x &lt; 2 [ * ] HG here stands for Hypergeometric. [ ** ] NB here stands for Negative Binomial....
View Full Document

This note was uploaded on 01/19/2011 for the course STATISTICS STAT 333 taught by Professor Menzhongxian during the Fall '10 term at Waterloo.

Ask a homework question - tutors are online