Independence (probability theory)When the occurrence of one event does not affect the likelihood of anotherIndependence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
Conditional probability distributionIn 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.Random variableVariable representing a random phenomenonA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.Event (probability theory)In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. An event consisting of only a single outcome is called an elementary event or an atomic event; that is, it is a singleton set.Conditional probabilityProbability of an event occurring, given that another event has already occurredIn probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion, or evidence) is already known to have occurred.
Conditional dependenceIn probability theory, conditional dependence is a relationship between two or more events that are dependent when a third event occurs. It is the opposite of conditional independence.
Probability theoryProbability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.Cumulative distribution functionProbability that random variable X is less than or equal to xCumulative distribution function for the exponential distributionCumulative distribution function for the normal distributionIn probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variableX{\displaystyle X}, or just distribution function of X{\displaystyle X}, evaluated at x{\displaystyle x}, is the probability that X{\displaystyle X} will take a value less than or equal to x{\displaystyle x}.
Joint probability distributionGiven random variablesX,Y,…{\displaystyle X,Y,\ldots }, that are defined on the same probability space, the multivariate or joint probability distribution for X,Y,…{\displaystyle X,Y,\ldots } is a probability distribution that gives the probability that each of X,Y,…{\displaystyle X,Y,\ldots } falls in any particular range or discrete set of values specified for that variable.
GraphoidA graphoid is a set of statements of the form, "X is irrelevant to Y given that we know Z" where X, Y and Z are sets of variables. The notion of "irrelevance" and "given that we know" may obtain different interpretations, including probabilistic, relational and correlational, depending on the application. These interpretations share common properties that can be captured by paths in graphs (hence the name "graphoid").Symmetric relationA symmetric relation is a type of binary relation. A homogeneous relation R {\displaystyle R} on a set X {\displaystyle X} is symmetric if: for all a {\displaystyle a} and b {\displaystyle b} in X {\displaystyle X} , a R b {\displaystyle aRb} if and only if b R a {\displaystyle bRa} , where the notation a R b {\displaystyle aRb} means that the ordered pair ( a , b ) {\displaystyle (a,b)} is in the relation R {\displaystyle R} .
Σ-algebraAlgebraic structure of set algebraIn mathematical analysis and in probability theory, a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In calculus and analysis, for example, σ-algebras are used to define the concept of sets with area or volume. In probability theory, they are used to define events for which a probability can be defined. In this way, σ-algebras help to formalize the notion of size.*As an Amazon Associate I earn from qualifying purchases.