Discrete Random Variables

It should be known that discrete numbers in mathematics and statistics are not ones that know how to sneak around. Instead, they are countable numbers, even countably infinite numbers. If numbers are not discrete then they are said to be continuous, or uncountable.

In the situation of a coin flip, we can assign a 1 to the outcome of a head, and a 0 to the outcome of a tail. Thus we have transformed the outcome of a coin flip to a discrete random variable, or something that is countable and random.

Discrete distributions must always have probabilities between 0 and 1 and all probabilities must sum to 1.

In math this is

0 < = p(x) < = 1
and Sum(p(x)) = 1