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Formulas and properties for various discrete and continuous probability distributions, including binomial, geometric, hypergeometric, poisson, negative binomial, uniform, normal, exponential, lognormal, gamma, beta, and weibull distributions. It includes the probability mass function, mean, variance, and moment generating functions for each distribution.

Typology: Study notes

Pre 2010

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Download Discrete & Continuous Distributions: PMFs & PDFs and more Study notes Mathematical Statistics in PDF only on Docsity! STAT 311 October 29, 2007 Discrete Distributions Distribution Probability Mass Function Mean Variance Moment Generating p(x) Function Binomial binomial(n, p) ( n x ) pxqn−x, x = 0, 1, · · · , n np npq (pet + q)n Geometric (i) pqx, x = 0, 1, · · · (i) q/p (i) q/p2 (i) p/(1− qet) G(p) (ii) pqy−1, y = 1, 2, · · · (ii) 1/p (ii) q/p2 (ii) pet/(1− qet) Hypergeometric ( a x )( N − a n− x ) / ( N n ) np (N − n) (N − 1) n p q complicated H(n, a, N) x = 0, 1, 2, · · · ,min(N − a, n) p = a/N Poisson Poisson(λ) λ xe−λ x! , x = 0, 1, · · · λ λ e λ(et−1) Negative Binomial (i) ( x + r − 1 x ) prqx, x = 0, 1, · · · (i) rq/p (i) rq/p2 (i) [p/(1− qet)]r NB(r, p) (ii) ( x− 1 r − 1 ) prqx−r, x = r, r + 1, · · · (ii) r/p (ii) rq/p2 (ii) [pet/(1− qet)]r