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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 ...
Continuous uniform. In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. [1]
v. t. e. In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [1][2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).
The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 − p. The Rademacher distribution, which takes value 1 with probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same ...
A beta distribution with shape parameters α = β = 1 is a continuous uniform distribution over the real numbers 0 to 1. A beta-binomial distribution with parameter n and shape parameters α = β = 1 is a discrete uniform distribution over the integers 0 to n.
Furthermore, it covers distributions that are neither discrete nor continuous nor mixtures of the two. An example of such distributions could be a mix of discrete and continuous distributions—for example, a random variable that is 0 with probability 1/2, and takes a random value from a normal distribution with probability 1/2.
Unlike a probability, a probability density function can take on values greater than one; for example, the continuous uniform distribution on the interval [0, 1/2] has probability density f(x) = 2 for 0 ≤ x ≤ 1/2 and f(x) = 0 elsewhere. The standard normal distribution has probability density. If a random variable X is given and its ...
The cumulative distribution function of a real-valued random variable is the function given by [2]: p. 77. (Eq.1) where the right-hand side represents the probability that the random variable takes on a value less than or equal to . The probability that lies in the semi-closed interval , where , is therefore [2]: p. 84.