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Dumasar kasapukan, variabel acak X disebut kontinyu mun fungsi sebaran kumulatifna kontinyu. That is equivalent to saying that Pr[X = a] = 0 for all real numbers a, i.e.: the probability that X attains the value a is zero, for any number a.
While for a discrete random variable one could say that an event with probability zero is impossible, this can not be said in the case of a continuous random variable, because then no value would be possible.
By another convention, the term "continuous random variable" is reserved for random variables that have probability density functions. A random variable with the Cantor distribution is continuous according to the first convention, and according to the second, is neither continuous nor discrete nor a weighted average of continuous and discrete random variables.
In practical applications random variables are often either discrete or continuous.