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Probability theory. Given two random variables that are defined on the same probability space, [1] the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables.
Conditional probability distribution. In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome given the occurrence of a particular event. Given two jointly distributed random variables and , the conditional probability distribution of given is the ...
Chain rule (probability) 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. This rule allows one to express a joint ...
Marginal distribution. In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.
Voronoi formula. In mathematics, a Voronoi formula is an equality involving Fourier coefficients of automorphic forms, with the coefficients twisted by additive characters on either side. It can be regarded as a Poisson summation formula for non-abelian groups. The Voronoi (summation) formula for GL (2) has long been a standard tool for ...
The multivariate normal distribution is said to be "non-degenerate" when the symmetric covariance matrix is positive definite. In this case the distribution has density [5] where is a real k -dimensional column vector and is the determinant of , also known as the generalized variance.
The joint entropy of a set of variables is less than or equal to the sum of the individual entropies of the variables in the set. This is an example of subadditivity. This inequality is an equality if and only if and are statistically independent. [3]: 30. {\displaystyle \mathrm {H} (X,Y)\leq \mathrm {H} (X)+\mathrm {H} (Y)}
A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model. It is constructed from the joint probability distribution of the random variable that (presumably) generated the observations.