Probability Theory – Cantor's Archive

Probability Theory

Why Probability Theory is Hard

It’s not because you’re stupid or weren’t concentrating in school

Probability Theory

Better-Than-Random Decisions in Uninformed Settings

Two envelopes with different amounts of money in them. Choose the better one with a higher chance than fifty-fifty!

Probability Theory

Transforming Scores Into Probability

How to show what subjective scores do and do not tell you about probability of success on the basis of their past performance

Pragmatism

Probability for Pragmatists

What does it mean that a probability is “correct” and how could you possibly know?

Number Theory

The Euler Totient Function

A Probabilistic Approach

Probability Theory

The Probabilistic Method

Maybe the most interesting proof method

Probability Theory

Monty Hall Revisited

How a causal framework can help you avoid the Monty Hall trap (and going home with a goat)

Poisson

The ‘Balls Into Bins’ Process and Its Poisson Approximation

A simple, yet flexible process to model numerous problems

Mathematical Modelling

The Time Evolution of a Particle’s Position

To determine the position of a particle can be a very challenging task. The obvious way is to look at it and see where it is at that time. However, as one can expect, measuring the position of a particle at every instance of time is very difficult (impossible). (A

Statistics

Maximum Likelihood Estimate

Part 2: Mixture Models

Probability Theory

Maximum Likelihood Estimate

Part 1: How to best fit a Gaussian

Probability Theory

A Wager, Rolling Restarts and Euler’s Number

Keep drawing integers from a random number generator (or a customized lottery machine) until you get a number that is smaller than the previous pick.