3.3 DISTRIBUTION FUNCTION
In order to describe continuous, discrete, and mixed random variables, we first introduce the distribution function, from which it is possible to derive either a pmf, a pdf, or a combination of both. Once specific families of random variables have been defined, there usually is no need to consider the abstract probability space 
(which, as mentioned before, may not exist). Instead, we can work directly with the distribution function defined for the probability space 
.
Definition: Distribution Function The distribution function with domain 
is the following probability:
where 
is a mapping of 
in the event space 
to a real number in [0, 1].
This probability assignment is yet another type of mapping: from a semi-open interval on to a point in the closed interval ...
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