Probability Theory
Why Probability Theory is Hard
It’s not because you’re stupid or weren’t concentrating in school
Probability Theory
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)
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
Poisson
The ‘Balls Into Bins’ Process and Its Poisson Approximation
A simple, yet flexible process to model numerous problems
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.