Probability & Statistics Ch.2 Section 1 Question 5

Solutions for “Probability and Statistics: The Science of Uncertainty” (Second Edition). These are solutions I have come up with; I offer no guarantee of accuracy.

Question

Let A and B be events, and let $X=\textit{I}_A \cdot \textit{I}_B$. Is X an indicator function? If yes, then of what event?

Solution

Yes, X is an indicator function as its only possible outcomes are 0 and 1.

X will output 1 when both $\textit{I}_A$ and $\textit{I}_B$ are 1 (i.e., when both events A and B occur).

Therefore, X is an indicator function of: $A \cap B$