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In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [ 1] A single outcome may be an element of many different events, [ 2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [ 3]
A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often represented in notation by is the set of all possible outcomes of a random phenomenon being observed. The sample space may be any set: a set of real numbers, a set of descriptive labels, a set of vectors ...
Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [ note 1][ 1][ 2] A simple example is the tossing of a fair (unbiased) coin.
The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 − p. The Rademacher distribution, which takes value 1 with probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same ...
Probability theory. Probability 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. Typically these axioms formalise probability ...
Convergence of random variables. In probability theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence in distribution, and almost sure convergence. The different notions of convergence capture different properties about the sequence, with some notions of ...
The Poisson distribution is an appropriate model if the following assumptions are true: k is the number of times an event occurs in an interval and k can take values 0, 1, 2, ... . The occurrence of one event does not affect the probability that a second event will occur. That is, events occur independently.
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. [ 1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one. A random experiment that has exactly two ...