Probability_Law_Tables

Probability_Law_Tables - DISCRETE DISTRIBUTIONS Moment...

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DISCRETE DISTRIBUTIONS Probability Law Parameters Probability distribution function mean variance Moment – generating function Bernoulli Trial X = 1, if S = success 0, if F = failure 0 p 1 p=P(success) q = 1-p =P(failure) p, x = 1 p(x) = q, x = 0 0, otherwise p pq pe t + q Binomial (n,p) X = # successes in n trials n = # trials 0 p 1 p=P(success) q = 1-p p(y)= n x p x q n x , x = 0,1,2,. .., n 0 , otherwise np npq ( pe t + q ) n Geometric (p) X = number of trials until the first success. 0 p 1 p= P(S) q = 1-p p(x) = pq x 1 , y = 1,2,3,. .. 0 , otherwise 1 p q p 2 pe t 1 qe t Poisson ( λ ) X = number of happenings per unit λ > 0 λ = average number of happenings per unit p(x) = e λ x x ! , x = 0,1, 2,. .. 0 , otherwise λ λ e ( e t 1) Negative Binomial X= # trials until the r-th success r > 0, integer 0 p 1 p=P(success) q = 1-p p(x)= x 1 r 1 p r q x r , y = r , r
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Probability_Law_Tables - DISCRETE DISTRIBUTIONS Moment...

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