Claude Shannon’s A mathematical theory of communication is an oft cited classic in information theory. Let’s dive in and try to tease apart the “why”s that are often overlooked when people build on top of the introduced theory. They are definitely things that I didn’t consider to be obvious without the benefit of reading the paper.
Deriving the Poisson Distribution
Where does the Poisson Distribution come from? A little bit of research1 tells us that the distribution was originally introduced by Abraham de Moivre in 1710 in an article called “On the Measurement of Chance, or, on the Probability of Events in Games Depending Upon Fortuitous Chance” 2 (not the original title). A few steps that will get us there is laid out below. Let’s start with a simple “rate” problem.
The Comcast Technician Problem
Given a set of tasks, incentives are often aligned towards dropping a task rather than allowing for perpetual accretion of delays.