University of Sheffield, MAS113 Introduction to Probability and Statistics

Welcome to the web pages for the probability section of MAS113 Introduction to Probability and Statistics. This covers the first semester and about the first three weeks of the second semester. Course notes (excluding some of the worked examples from the lectures), exercises and solutions will appear here, in PDF format.

Information about the statistics section, lectured by Prof Jeremy Oakley, is available on MOLE.

Information about the course

For now, timetable information is provisional. In semester 1, lectures are on Mondays at 9am in Alfred Denny Building Lecture Theatre 2 and Tuesdays at 12 noon in Dainton Lecture Theatre 1.

There will be one other session in each week. In weeks 1 and 2 it will be a computer class, giving an introduction to the software package R, and in weeks 3 to 12 (excluding week 7, which is a reading week) it will be a tutorial. These sessions will be on Wednesdays, at either 9am or 11am depending on 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.

For the tutorials, I will announce which questions from the exercise booklet you should look at in advance of the class. You should have a look at the questions before the class so that you have a good idea what you want to ask about; this is a much better use of the time available than if you only look at them for the first time in the class.

If you cannot make the time of your allocated group for a good reason, please email me and I will see whether I can move you.

Homework will be set after tutorials every other week, to be handed the following week. The work should be handed in to folders which will be placed outside room I9. The plan is that the homework deadlines in semester 1 will be on the Mondays 16 October, 30 October, 13 November, 27 November and 11 December. The homework is for feedback purposes.

Assessment is by an exam at the end of the module and online tests. The online tests for the module will be available on MOLE. The online tests in semester 1 will have deadlines on Fridays 6 October (not for assessment) and then 20 October, 3 November, 1 December and 15 December.

To contact the lecturer, email My office is I9, on the fifth floor of the Hicks Building.

A discussion board for this module is available on MOLE.

In some lectures I will use the L3cture app to run (non-compulsory) polls and mini-quizzes.

Lecture notes

Course guide, and introductory slides, which cover the same material.

Notes for the probability part of the course

Alternatively, sections of the notes are available separately:
Notes part 1 (sections 1 to 6: introduction; measure; probability as measure; assigning probabilities; conditional probability).
Notes part 2 (sections 7 to 9: discrete random variables; mean and variance; binomial, Poisson and geometric distributions).
Notes part 3 (sections 10 to 12: multivariate discrete distributions; covariance and correlation; the multinomial).
Notes part 4 (sections 13 to 15: continuous random variables; mean and variance in the continuous case; exponential and normal distributions).
Notes part 5 (sections 16 to 19: sums of independent random variables; law of large numbers; moment generating functions; Central Limit Theorem).

Proofs of theorems lectured so far.

Slides will appear here after the relevant section has been lectured:

Introduction to R (for the computer classes in weeks 1 and 2).

Supplementary notes: more detailed definition of measure, permutations and combinations, more on subjective probability, the Normal and Cauchy distributions.


Booklet of exercises for the course. This covers the whole of the probability section of the course.

Solutions to exercises

Solutions will appear here after homework deadlines. Solutions so far (all solutions now available).

Past exam solutions

These will appear on MOLE before the exam. The exam papers themselves can be found on the SoMaS past papers page.


The materials for this course are largely based on those used by Prof Jeremy Oakley and Prof Dave Applebaum in previous years.

My home page
School of Mathematics and Statistics current students page

Last updated 5 April 2018.