Chapter 2 Section 1 Question 13

Question

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

Answer

Author: Mohammad-Ali Bandzar| Date:Oct 14 2020

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.

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.