Computational Physics

Computational Problems Involving Probability

In semester 5, we looked at a number of problems involving basic probability. In this module we will build on this and look at problems requiring more advanced treatment, in particular, the use of discrete and continuous probability distributions.

Review of Probability Concepts
Summary of probability concepts with python implementations of examples.
- Fundamental concepts in probability
- Laws of probability
- Handout
- Presentation
Conditional Probability and Bayes Rule
Conditional probability and Bayes Theorem
- Non-independent events
- Bayes Theorem
- Handout
- Presentation
The Nearly Intoxicated Waiter
A probability problem dealing with permutations.
- Open in Colab
Unhappy Couple Flight
A probability problem that demonstrates you should not take martial advice from a mathematician.
- Open in Colab
Balls into Bins
A probability problem.
- Open in Colab
Dealing Cards
A probability problem dealing with random partitioning where sum of elements in each partition is of interest.
- Open in Colab
Balls into Bins
A probability problem dealing with random partitioning where size of each partition is of interest.
- Open in Colab
Discrete Random Variables
General theory of discrete random variables and some important discrete probability distributions.
- Discrete random variables
- Uniform, Bernoulli, Binomial, Poisson
- Handout
- Presentation
Continuous Random Variables
General theory of continuous random variables and some important continuous probability distributions.
- Continuous random variables
- Uniform, Exponential, Normal
- Handout
- Presentation
Probability Distributions
A set of short problems based on discrete and continuous probability distributions.
- Open in Colab

Computational Problems Involving Probability

Review of Probability Concepts

Conditional Probability and Bayes Rule

The Nearly Intoxicated Waiter

Unhappy Couple Flight

Balls into Bins

Dealing Cards

Balls into Bins

Discrete Random Variables

Continuous Random Variables

Probability Distributions