Practise projects: Markov chains in discrete time
The panel on the right of this page contains links to some more challenging programming exercises that require you to use the material that is covered in this chapter. You are strongly encouraged to create a new python notebook for each of the problems listed here that you attempt. Put all the code you write and the explanations of the mathematical ideas you use in the notebook. Please note that there is an enormous ammount of information about python available online and we fully expect you to take advantage of this rich information stream. Some (brief) introductions to the python notebook system are provided below:
- Introductory videos on running the notebook and writing in the notebook
- Introductory video on writing equations with the notebook, notes on the markdown language you can use for writing plain text and a short summary of the key markdown commands.
- List of latex commands that can be used to typeset mathematical equations in the jupyter notebook system
In addition the buttons below allow you to access resources on the python syntax for key programming concepts
Variables Functions Logic Loops Lists GraphsIf you would like to download the python notebook system onto your own laptop you can find it here:
https://www.continuum.io/downloadsThere are some instructions on how to install it on your computer in this video
(Level 0) Deriving the probability of ruin in gamblers ruin |
topic: Gamblers ruin |
author: G. Tribello |
(Level 0) Deriving the expected length of the game in the gamblers ruin problem |
topic: Gamblers ruin |
author: G. Tribello |
(Level 1) A programming exercise on simulating a one dimensional random walk. |
topic: Gamblers ruin |
author: G. Tribello |
(Level 2) A programming exercise on simulating an ergodic Markov chain. |
topic: Ergodic Markov chains |
author: G. Tribello |
(Level 3) A programming exercise that involves investigating a periodic Markov chain (this is a harder version of the level 2 problem). |
topic: Ergodic Markov chains |
author: G. Tribello |