Indicator Random Variable

A Discrete Random Variable that is split into two sets used to describe if an event will happen.

Example

Consider events $A,B$ and Indicator RVs $I_A,I_B$ Show that $1-I_A$ is an indicator RV:

Soln

$$\{\begin{array}{ll}1& S\in A^c\\ 0& S\in A\end{array}$$

Example 2

Show that $I_A\times I_B$ is an indicator RV:

Soln

$$\{\begin{array}{ll}1& s\in A\cap s\in B⟹s\in A\cap B\\ 0& s\in (A\cap B{)}^c⟹s\in A^c\cup B^c\end{array}$$