---
title: Dirt in the Mouse & Glivenko-Cantelli Theorem
date: '2008-06-15'
slug: dirt-in-the-mouse-glivenko-cantelli-theorem
---

There was something wrong with the wheel of my mouse these days: it could not control the scrolling of a page very well. Today I found a screwdriver and opened the mouse. Then I knew the reason: there was a lot of dirt beneath the cover!

However, obviously the dirt would not follow a `B(n, p = 0.5)` distribution. The two proportions of the dirt in front and back of the wheel were not equal -- there was much more dirt in the back. Why?

> The [Glivenko-Cantelli Theorem](http://en.wikipedia.org/wiki/Glivenko-Cantelli_theorem) tells us that the empirical distribution converges to the true distribution almost surely.

So what? The proportions of the dirt has revealed my habit of using the mouse, as I have used it for too many times. What I usually do is to scroll _down_ a page, and rarely will I scroll _up_ -- that is the real distribution, and the dirt in the mouse has recorded the empirical distribution day by day. If I am serious enough, I can get the numbers of the weight and estimate the parameter _p_ in the Binomial distribution. (Perhaps [Michal](http://bojan.3e.pl/weblog) will again suggest me do this. :grin: )
