A variate is a generalization of the concept of a random variable that is defined without reference to a particular type of probabilistic experiment. It is defined as the set of all random variables that obey a given probabilistic law. It is common practice to denote a variate with a capital letter (most commonly X). The set of all values that X can take is then called the range, denoted ℜ_X . Specific elements in the range of X are called quantiles and denoted x, and the probability that a variate X assumes the value x is denoted P(X = x).
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