A random variable X is called continuous if its set of possible values is uncountable, and the chance that it takes any particular value is zero (P(X=x)=0 for every real number x). A random variable is continuous if and only if its cumulative probability distribution function is a continuous function.
Overview
From Mood et al. (page 60, 1974):
"A random variable X is called continuous if there exists a function fX (.) such that
for every real number x. The cumulative distribution function FX (.) of a continuous random variable X is called absolutely continuous".
Excerpt reference: Glossary of Statistical Terms from berkeley.edu
Tag usage
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