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Distribution Table - Special Discrete Distributions...

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Special Discrete Distributions Notation and Parameters p.f. Mean Variance m.g.f. Binomial X ! 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 ! Bernoulli ! p " p x q 1 " x p pq pe t ! q 0 " p " 1 x # 0,1 q # 1 " p Negative Binomial X ! NB ! k , p " " k x ! " p k ! " q " x kq p kq p 2 ! p 1 " qe t " k 0 " p " 1 q # 1 " p x # 0,1,... t " " log q Geometric X ! GEO ! p " pq x q / p q / p 2 p 1 " qe t 0 " p " 1 x # 0,1,... t " " log q q # 1 " p
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Special Discrete Distributions Notation and Parameters p.f. Mean Variance m.g.f. Hypergeometric X ! 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 # 0,1, # , N Poisson X ! POI ! ! " e " ! ! x / x ! ! ! e ! ! e t " 1 " ! $ 0 x # 0,1, # Discrete Uniform X ! DU ! N " 1/ N N ! 1 2 N 2 " 1 12 1 N e t " e ! N ! 1 " t 1 " e t N # 1,2, # x # 1,2, # , N t # 0 * Not Tractable
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Special Continuous Distributions Notation and Parameters p.d.f. Mean Variance m.g.f. Uniform X ! UNIF ! a , b " 1/ ! b " a " a ! b 2 ! b " a " 2 12 e bt " e at ! b " a " t a " b a $ x $ b t # 0 Normal X ! N ! ! , " 2 " 1 2 # " e " $! x " ! " / " % 2 /2 ! " 2 e ! t ! " 2 t 2 /2 " 2 $ 0 Gamma X ! GAM ! $ , % " 1 % $ % ! $ " x $ " 1 e " x / % $% $% 2 ! 1 " % t " " $ % $ 0 x $ 0 $ $ 0 t " 1/ % Inverted Gamma X ! IG ! $ , % " 1 % $ % ! $ " x " $ " 1 e " 1/ ! % x " 1 % ! $ " 1 " 1 % 2 ! $ " 1 " 2 ! $ " 2 " * % $ 0 $ $ 0 x $ 0
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Special Continuous Distributions Notation and Parameters p.d.f. Mean Variance m.g.f.
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