Common Probability Functions

Common Probability Functions - Summary of Common...

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Summary of Common Probability Distributions DISCRETE VARIABLES Binomial P(x) = n! x! n x ( ) ! p x (1 p) n x x = number of succeses p = probability of success n = number of independent trials μ x = n × p σ x 2 = n × p × (1 p) Geometric P(x) = p × (1 p) x 1 = probability of a success on the xth independent trial p = probability of success μ x = 1 p = "return period" σ x 2 = 1 p p 2 Negative Binomial P(x,r) = x 1 r 1 p r (1 p) x r = probability of taking x trials to get r successes p = probability of success μ x = r p σ x 2 = r(1 p) p 2
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Poisson P(x) = e −λ λ x x! = probability of x successes as n → ∞ μ x = λ = np = ν t = expected number of successes in time t ν = frequency of successes σ x 2 = λ Hypergeometric P(x) = R x N R n x N n N = total number of items in population R = number of items in the population with a certain characteristic
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This note was uploaded on 10/22/2011 for the course ENG 101 taught by Professor Yukov during the Spring '11 term at UCLA.

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Common Probability Functions - Summary of Common...

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