11 Facts About Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.

Probability distribution is a mathematical description of the probabilities of events, subsets of the sample space.

The cumulative distribution function is the area under the probability density function from to, as described by the picture to the right.

Probability distribution can be described in various forms, such as by a probability mass function or a cumulative distribution function.

The normal distribution is a commonly encountered absolutely continuous probability distribution.

Probability distribution whose sample space is one-dimensional is called univariate, while a distribution whose sample space is a vector space of dimension 2 or more is called multivariate.

Any probability distribution can be decomposed as the sum of a discrete, an absolutely continuous and a singular continuous distribution, and thus any cumulative distribution function admits a decomposition as the sum of the three according cumulative distribution functions.

Additionally, the discrete uniform distribution is commonly used in computer programs that make equal-probability random selections between a number of choices.

Special case is the discrete Probability distribution of a random variable that can take on only one fixed value; in other words, it is a deterministic Probability distribution.

An absolutely continuous probability distribution is a probability distribution on the real numbers with uncountably many possible values, such as a whole interval in the real line, and where the probability of any event can be expressed as an integral.

Some authors however use the term "continuous distribution" to denote all distributions whose cumulative distribution function is absolutely continuous, i e refer to absolutely continuous distributions as continuous distributions.