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Discrete Distributions


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(Discrete) Uniform distribution
Discrete distribution where all elements of a finite set are equally likely.
Bernoulli trial
An experiment whose random outcome can be either "success" or "failure".
Bernoulli distribution
Discrete distribution which takes value 1 with probability p and value 0 with probability q = 1 − p.
Binomial distribution
Describes the number of successes in a series of independent Bernoulli trials with the same probability of success.
Geometric distribution
Describes in which attempt the first success in a series of independent Bernoulli trials occurs.
Hypergeometric distribution
Describes the probability to draw k white balls in n draws without replacement from an urn containing K white balls and N balls in total.
Poisson distribution
Describes how likely it is that a certain number of events occurs in a time interval when the probability per time interval is known (and the possible number of events is "large").
Negative binomial distribution
Describes in which attempt the r-th success in a series of independent Bernoulli trials occurs.
Poisson binomial distribution
Describes the number of successes in a series of independent Bernoulli trials with different success probabilities.
Rademacher distribution
Discrete distribution which takes value 1 with probability 1/2 and value −1 with probability 1/2.
Categorical distribution
Generalization of the Bernoulli distribution for a discrete random variable with r possible outcomes having individual probabilities.
Multinomial distribution
Generalization of the binomial distribution for a series of independent trials with r outcomes having individual probabilities.