Probability theory

Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins.

In probability theory, a distribution is said to be stable (or a random variable is said to be stable) if a linear combination of two independent copies of a random sample has the same distribution, up to location and scale parameters.

A stochastic event or system is one that is unpredictable because of a random variable.

In probability theory and statistics, a Gaussian process is a statistical model where observations occur in a continuous domain, e.

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the x-axis.

In Kolmogorov's probability theory, the probability P of some event E, denoted , is usually defined such that P satisfies the Kolmogorov axioms, named after the Russian mathematician Andrey Kolmogorov, which are described below.

In information theory, the typical set is a set of sequences whose probability is close to two raised to the negative power of the entropy of their source distribution.

Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms.

In information theory, systems are modeled by a transmitter, channel, and receiver.

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure.

Principles of the Theory of Probability is a 1939 book by the philosopher Ernest Nagel.

Benford's law, also called the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data.

In combinatorics (combinatorial mathematics), the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as The principle is more clearly seen in the case of three sets, which for the sets A, B and C is given by Generalizing the results of these examples gives the principle of inclusion–exclusion.

In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator.

In probability theory, conditional dependence is a relationship between two or more events that are dependent when a third event occurs.

In probability theory, two events R and B are conditionally independent given a third event Y precisely if the occurrence or non-occurrence of R and the occurrence or non-occurrence of B are independent events in their conditional probability distribution given Y.