Indicator variable

A Random variable that has a support of $\{0,1\}$.

The PMF of an indicator usually depends on an event $A$ occurring or not. If $P(A)$ is nonzero, then the indicator has a Bernoulli distribution. A “fundamental bridge” exists between the probability of event $A$ occurring and the Expectation of this indicator:

$$P(A)=\mathbb{E}(I_A)$$

This allows us to calculate the expectation of a r.v. using indicator variables, for example.