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RandomVariable
In probability theory, a random variable is a function that assigns a real number to each realization of a random experiment. The set of possible outcomes is called the sample space.
Formally, let's denote the sample space as
where
This definition implies that to each element
A key concept related to random variables is that of their distribution, which gives the probabilities associated with the possible values of the random variable. For a discrete random variable, the distribution is given by a probability mass function, while for a continuous random variable, it is given by a probability density function.
Furthermore, random variables can be characterized by various quantities such as their expected value (or "mean"), variance, and higher moments, which provide information about the "average" value, spread, and shape of the distribution, respectively.