discrete and continuous random variables

Distinguishing between random variables:
(See discrete and continuous variables)

A discrete random variable has a support which is finite or countably infinite.
The probability of a discrete random variable is described by a probability mass function.

A continuous random variable has a support which is uncountably infinite.
The probability of a continuous random variable is described by a probability density function.
No single value within the support of a continuous random variable has positive probability.