Category: Introduction

Introduction XII -Order Statistics

We've used order statistics already when we covered auction theory┬ábut some of you might not have known what order statistics are. I hope I can enlighten those┬átoday. Order Statistics What are Order Statistics? Order statistics are what the name says. They are the probability that a given value of i.i.d random variables is the nth … Continue reading Introduction XII -Order Statistics

Introduction XI – Distributions and what they model

A lot of random variables follow a known distribution. It is therefore good to know some of the most common distributions and what they model. Remembering their PMFs or PDFs is not necessary. Uniform Distribution The uniform distribution is probably one of the most famous distributions. It models a random variable with equally likely outcomes. … Continue reading Introduction XI – Distributions and what they model

Introduction X – Covariance and Correlation

We often want to get a picture of how the relationship between two random variables is. In many cases or more precise in cases where the random variables are independent, we can get a picture of their relationship by inspecting the joint distribution, however that, as already mentioned, just works when the two random variables … Continue reading Introduction X – Covariance and Correlation

Introduction IX – Joint Distributions

In the past we always worked with just one random variable at a time. Unfortunately that is not always what we want to do. Although unfortunately doesn't quite fit here as it actually becomes more interesting when we observe two or more random variables at the same time, it was what I first thought. I … Continue reading Introduction IX – Joint Distributions

Introduction VIII – Central Limit Theorem

Estimates are sometime our only option. We almost never have the whole population to our hands and can therefore almost never poll the whole population or calculate things given the whole population. That might be because the logistical effort would be to big (imagine one would poll all 300 million people in the US every … Continue reading Introduction VIII – Central Limit Theorem

Introduction VII – Law of Large Numbers

Introduction VII – Law of Large Numbers

Our intuition can be mathematical Sometime maths can be quite an intuitive thing. The Law of Large Numbers is such a case. Law of Large Numbers (LLN) The LLN tells us that when the number of trials increases, the sample mean approaches the population mean. Or in more mathematical terms: $latex as \;n\rightarrow \infty,\; \overline … Continue reading Introduction VII – Law of Large Numbers

Introduction VI – Continuous Random Variables

Welcome to the power of Continuous Random Variables Discrete Random Variables were our entry into the real world of probability. They enabled us to model a random variable and to do our first real calculations. We learned how to summarise a distribution in just one number, the mean, and how we can improve our summary … Continue reading Introduction VI – Continuous Random Variables