For example, a discrete random variable
X can take on a limited number of outcomes
x1,
x2, …,
xn (
n possible outcomes), or a discrete random variable
Y can take on an unlimited number of outcomes
y1,
y2, … (without end).
1 Because we can count all the possible outcomes of
X and
Y (even if we go on forever in the case of
Y), both
X and
Y satisfy the definition of a discrete random variable. By contrast, we cannot count the outcomes of a
continuous random variable. We cannot describe the possible outcomes of a continuous random variable
Z with a list
z1,
z2, … because the outcome (
z1 +
z2)/2, not in the list, would always be possible. Rate of return is an example of a continuous random variable.