Probability distribution function
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Depending upon which text is consulted, a probability distribution function is any of:
- a probability distribution function,
- a cumulative distribution function,
- a probability mass function, or
- a probability density function.
The similar term probability function may mean any of the above and, in addition,
- a probability measure function, as in a probability space, where the domain of the function is the set of events.
Let P:∆→ℝ be a probability function and ∆ is the class of subsets of any event space S connected to a random experiment E. Now let X be a random variable defined on S.The distribution function of the random variable X with respect to the probability space (S,∆,P) is a real valued function F(x)=P(-∞≤X≤x),for all x∈(-∞,∞). The range of the distribution function is a subset of [0,1].