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In probability theory, the joint probability distribution is the probability distribution of all possible pairs of outputs of two random variables that are defined on the same probability space. The joint distribution can just as well be considered for any given number of random variables.
One can compute this directly, without using a probability distribution (distribution-free classifier); one can estimate the probability of a label given an observation, (| =) (discriminative model), and base classification on that; or one can estimate the joint distribution (,) (generative model), from that compute the conditional probability ...
In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0, 1]. Copulas are used to describe/model the dependence (inter-correlation) between random variables . [ 1 ]
In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it were a continuous distribution. The Kent distribution on the two-dimensional sphere.
A product distribution is a probability distribution constructed ... to the Wishart distribution. The latter is the joint ... Mathematics . 18 (4): 721– 737. ...
Given a known joint distribution of two discrete random variables, say, X and Y, the marginal distribution of either variable – X for example – is the probability distribution of X when the values of Y are not taken into consideration. This can be calculated by summing the joint probability distribution over all values of Y.
Formally, an exchangeable sequence of random variables is a finite or infinite sequence X 1, X 2, X 3, ... of random variables such that for any finite permutation σ of the indices 1, 2, 3, ..., (the permutation acts on only finitely many indices, with the rest fixed), the joint probability distribution of the permuted sequence