Probability & Statistics Ch.2 Section 1 Question 13

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

Suppose the sample space S is finite, of size m. How many different indicator functions can be defined on S?

Solution

The number of unique indicator functions we can define on S will be equal to the number of possible subsets of S that we can create.

The formula to find the maximum number of subsets (including the empty set) is $2^n$ where n represents the number of elements in your set.

In this case, we could define $2^m$ many different indicator functions on S.