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Tabledist - Special Discrete Distributions Notation and Parameters Binomial X v BIN(n p 0

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Special Discrete Distributions Notation and Parameters p.f. Mean Variance m.g.f. Binomial X v BIN ( n,p ) ¡ n x ¢ p x q n x np npq ( pe t + q ) n 0 <p< 1 x =0 , 1 ,...,n q =1 p Bernoulli X v Bernoulli ( p ) p x q 1 x pp qp e t + q 0 1 x , 1 q p Negative Binomial X v NB ( k,p ) ¡ k x ¢ p k ( q ) x kq p kq p 2 ( p 1 qe t ) k 0 1 q px , 1 ,... t < log q Geometric X v GEO ( p ) pq x q/p q/p 2 p 1 qe t 0 1 x , 1 t < log q q p

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Special Discrete Distributions Notation and Parameters p.f. Mean Variance m.g.f. Hypergeometric X v HYP ( n,M,N ) ¡ M x ¢¡ N M n x ¢ / ¡ N n ¢ nM/N n M N (1 M N ) N n N 1 * n =1 , 2 , ··· ,N x =0 , 1 , ,n M , 1 , Poisson X v POI ( μ ) e μ μ x /x ! μμ e μ ( e t 1) μ > 0 x , 1 , Discrete Uniform X v DU ( N )1 /N N +1 2 N 2 1 12 1 N e t e ( N +1) t 1 e t N , 2 , x , 2 , t 6 * Not Tractable
Special Continuous Distributions Notation and Parameters p.d.f. Mean Variance m.g.f. Uniform X v UNIF ( a, b )1 / ( b a ) a + b 2 ( b a ) 2 12 e bt e at ( b a ) t a<b a x bt 6 =0 Normal X v N ( μ , σ 2 ) 1 2

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This note was uploaded on 04/27/2010 for the course STAT 330 taught by Professor Paulasmith during the Fall '08 term at Waterloo.

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Tabledist - Special Discrete Distributions Notation and Parameters Binomial X v BIN(n p 0

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