Geometric and Exponential

Forgetful distributions

This week we’ll deal with memory. More specifically, we’ll tackle the question of when a distribution do not have any memory whatsoever, meaning that it doesn’t depend on past experience in any way. It turns out that there is a unique continuous distribution with this property, the exponential distribution, and... [Read More]

Uniform

The universality of the uniform

Today I’d like to talk about the uniform distribution. It might seem a bit weird to dedicate an entire post to such a thing as it’s arguably one of the simplest distributions there are. But where the definition isn’t that interesting, it has a very fundamental property in that it... [Read More]

Poisson

The law of small numbers

In these first few posts I’ll cover a few common distributions and note their interesting properties. I’ll try to follow standard notation here, so that capital letters $X,Y,Z$ will denote random variables, which are represented as functions $X\colon\Omega\to\mathbb R$ for some sample probability space $\Omega$. $P(A)$ will be the probability... [Read More]