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.

中文翻译：

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康托尔分布的几何推导

摘要

对于概率和统计学的学生来说，康托尔分布提供了一个有用的例子，说明了实线上的连续概率分布，它不能通过积分它的导数或任何密度函数来获得。虽然通常被视为一个高级主题，但我们表明，关于康托尔分布的基本事实可以通过使用简单几何和递归的一系列均匀分布以及高级微积分的一个基本结果严格推导出来。