Change of Variable Formula: Devil's Staircase

This lecture covers a change of variable formula for CDFs and PDFs, showing how to compute the CDF and PDF of a transformed random variable. It then introduces the Devil's Staircase, a strange CDF constructed using the Cantor set, and discusses the properties of this unique function. The Devil's Staircase is a continuous function that is flat almost everywhere, making it neither a discrete nor a continuous random variable. The lecture emphasizes the importance of using CDFs to ensure well-defined probability distributions, even in unconventional cases.