# Distribution

* normal
* exponential
* linear
* Cauchy

## Probability distribution

**Probability distribution** is a description of a random phenomenon in terms of the probabilities of events.

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

For instance, in a fair coin toss experiment, if the random variable $$X$$ is used to denote the outcome of a coin toss, then the probability distribution of $$X$$ would take the value 0.5 for `X = heads`, and 0.5 for `X = tails`.

Examples of random phenomena can include the results of an experiment or survey.

A probability distribution is specified in terms of an underlying **sample space**, which is the set of all possible outcomes of the random phenomenon being observed. The sample space may be the set of real numbers, vectors, a list of non-numerical values; the sample space of a coin toss would be `{heads, tails}`.

Probability distributions are generally divided into 2 classes:

* discrete probability distribution
* continuous probability distribution

**Discrete probability distribution**, applicable to the experiments where the set of possible outcomes is discrete, can be represented by a discrete list of the probabilities of the outcomes, known as a _probability mass function_.

**Continuous probability distribution**, applicable to the experiments where the set of possible outcomes can take on values in a continuous range, is typically described by _probability density functions_ (with the probability of any individual outcome actually being 0).

**The normal distribution** (aka Gaussian, Gauss, Laplace–Gauss distribution) is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.

A random variable with a normal distribution is said to be normally distributed and is called a _normal deviate_.

More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures.

**Univariate distribution** is a probability distribution whose sample space is one dimensional (e.g. real numbers, list of labels, ordered labels or binary). A univariate distribution gives the probabilities of a single random variable taking on various alternative values. Important and commonly encountered univariate probability distributions include _binomial distribution_,_hypergeometric distribution_ and _normal distribution_.

**Multivariate distribution** is a probability distribution whose sample space is a vector space of two or more dimensions. A multivariate distribution (a joint probability distribution) gives the probabilities of a random vector – a list of two or more random variables – taking on various combinations of values. Commonly encountered multivariate distribution is _multivariate normal distribution_
