A Geometric Derivation of the Cantor Distribution

Abstract

For students of probability and statistics, the Cantor distribution provides a useful example of a continuous probability distribution on the real line which cannot be obtained by integrating its derivative or indeed any density function. While usually treated as an advanced topic, we show that the basic facts about the Cantor distribution can be rigorously derived from a sequence of uniform distributions using simple geometry and recursion, together with one basic result from advanced calculus.