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In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number n of outcome values are equally likely to be observed. Thus every one of the n outcome values has equal probability 1/n. Intuitively, a discrete uniform distribution is "a known, finite number ...
The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
Well-known families in which the functional form of the distribution is consistent throughout the family include the following: Normal distribution; Elliptical distributions; Cauchy distribution; Uniform distribution (continuous) Uniform distribution (discrete) Logistic distribution; Laplace distribution; Student's t-distribution
A beta-binomial distribution with parameter n and shape parameters α = β = 1 is a discrete uniform distribution over the integers 0 to n. A Student's t-distribution with one degree of freedom ( v = 1) is a Cauchy distribution with location parameter x = 0 and scale parameter γ = 1.
Equiprobability is a property for a collection of events that each have the same probability of occurring. [1] In statistics and probability theory it is applied in the discrete uniform distribution and the equidistribution theorem for rational numbers.
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .
In probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random.