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Probability theory. In probability theory, the sample space (also called sample description space, [1] possibility space, [2] or outcome space[3]) of an experiment or random trial is the set of all possible outcomes or results of that experiment. [4] A sample space is usually denoted using set notation, and the possible ordered outcomes, or ...
t. e. In probability theory, a probability space or a probability triple is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die. A probability space consists of three elements: [1][2] A sample space, Ω {\displaystyle \Omega }
t. e. In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [1][2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). [3]
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
Definition. A random variable is a measurable function from a sample space as a set of possible outcomes to a measurable space . The technical axiomatic definition requires the sample space to be a sample space of a probability triple (see the measure-theoretic definition).
e. 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]
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