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  2. Sample space - Wikipedia

    en.wikipedia.org/wiki/Sample_space

    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 sample points, [5] are ...

  3. Event (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Event_(probability_theory)

    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]

  4. σ-algebra - Wikipedia

    en.wikipedia.org/wiki/Σ-algebra

    σ-algebra. In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair is called a measurable space . A σ-algebra of subsets is a set algebra of subsets; elements of the latter ...

  5. Law of total probability - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_probability

    The law of total probability is [1] a theorem that states, in its discrete case, if is a finite or countably infinite set of mutually exclusive and collectively exhaustive events, then for any event : or, alternatively, [1] where, for any , if , then these terms are simply omitted from the summation since is finite.

  6. Random variable - Wikipedia

    en.wikipedia.org/wiki/Random_variable

    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 ). A random variable is often denoted by capital Roman letters such as .

  7. Probability space - Wikipedia

    en.wikipedia.org/wiki/Probability_space

    A probability space is a mathematical triplet that presents a model for a particular class of real-world situations. As with other models, its author ultimately defines which elements , , and will contain. The sample space is the set of all possible outcomes. An outcome is the result of a single execution of the model.

  8. Outcome (probability) - Wikipedia

    en.wikipedia.org/wiki/Outcome_(probability)

    v. t. e. In probability theory, an outcome is a possible result of an experiment or trial. [1] Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space.

  9. Space (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Space_(mathematics)

    Space (mathematics) In mathematics, a space is a set (sometimes known as a universe) with a definition ( structure) of relationships among the elements of the set. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion ...