Some Properties of the Cantor Distribution

The Cantor distribution is defined as a random series $$\frac{1-\phi}{\phi}\sum_{k\ge1}X_k\phi^k,$$ where $\phi$ is a parameter and $X$ is random variable that takes the values 0 and 1 with probability $1/2$. The moments and order statis- tics are discussed, as well as a ``Fibonacci'' variation. Connections to certain trees and splitting processes are also mentioned.