Indicator function and Random variable

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Difference between Indicator function and Random variable

Indicator function vs. Random variable

In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. A 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.

Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.

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Function (mathematics)

In mathematics, a function from a set to a set assigns to each element of exactly one element of.

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Iverson bracket

In mathematics, the Iverson bracket, named after Kenneth E. Iverson, is a notation that generalises the Kronecker delta, which is the Iverson bracket of the statement.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Measure (mathematics)

In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events.

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Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment.

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Probability space

In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that provides a formal model of a random process or "experiment".

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Random variable

A 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.

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Range of a function

In mathematics, the range of a function may refer to either of two closely related concepts.

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Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

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Set (mathematics)

In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

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Variance

In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.

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