University of Sheffield, MAS275 Probability Modelling

Welcome to the web pages for MAS275 Probability Modelling. Course notes, exercises and solutions will appear here, in PDF format.

During the coronavirus outbreak, no inperson teaching will be delivered. Please do not come to lectures, tutorials, or office hours until receiving official instruction from the university that it is safe to do so!

Supplementary files due to online teaching

Information about the course

The lectures for this course are on Tuesdays at 12 in Diamonds Lecture Theatre 2 and Fridays at 11 in Hicks Lecture Theatre 7.

Tutorials will be held every other week, starting in the second week of the course. They will be Tuesdays at 16:00; Wednesdays at 12:00; or Thursdays at 12:00 depending which group you are in; you can find out which group you are in and the name of your group's tutors at the SoMaS tutorial groups page. This will also tell you where the classes are.

Homework will be set to be handed in for weeks 3, 5, 7, 9 and 11: the folders will be left outside my office (G39b Hicks) from 11am on Tuesday and you should hand the work in by 2pm on Wednesday. The marking will be for feedback rather than for formal assessment.

To contact the lecturer, email My office is I18 in the Hicks Building. My office hour for the course is 12:00 - 13:00 on Fridays.

A discussion board for this module will be available on MOLEdiscussion.


Assessment for the course will be by a 2 hour closed book exam.

Lecture notes

The notes are divided into six sections. Notes for each section are available from the links below:

There is also some extra material which may be useful.

The Kruskal count card trick is related to the proof of Theorem 12. In the lecture I showed Ravi Montenegro's page demonstrating the trick at the University of Massachusetts Lowell.

Slides for Markov Monopoly (Example 21)

Link to Page and Brin paper describing Google PageRank

Lecture Examples (complete)

Mini-web examples for PageRank (examples 26 and 27): 1,2,3


Exercise booklet for the course. This covers the whole course.

Solutions to exercises

Sample code for programming exercises (will appear here)

R code for simulating a basic Poisson process

Past exams

They can be found on the SoMaS past papers page.

Here are some solutions: 2019,2018,2017,2016.