Welcome to the web pages for the probability section of MAS113 Introduction to Probability and Statistics. This covers the first semester and 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.

There will be two **lectures** each week. In semester 2, these will be on Mondays at 09:00 in Alfred Denny Building Lecture Theatre 2 and Thursdays at 16:00 in Dainton Building Lecture Theatre 1.

There will be one other session in each week. In weeks 1 to 4, corresponding to the probability part of the course, it will be on Mondays at either 13:00, 15:00 or 16:00; 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. Homework deadlines in semester 2 will be Mondays 11 February and 25 February. The homework is for feedback purposes.

**Assessment** is by an exam at the end of the module and online tests, together with R practicals on the statistics material in semester 2. The online tests for the module will be available on MOLE. The online tests on semester 2 will have deadlines on Fridays 8 February and 22 February.

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: continuous random variables; mean and variance in the continuous case; exponential and normal distributions).
- Notes part 4 (sections 13 to 15: multivariate discrete distributions; covariance and correlation; the multinomial).
- Notes part 5 (sections 16 to 19: sums of independent random variables; law of large numbers; moment generating functions; Central Limit Theorem).

Details of proofs of theorems and of worked examples will be available after they are lectured:

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

- Slides part 1 (covering sections 1 to 3)
- Slides part 2 (covering sections 4 to 6)
- Slides part 3 (covering sections 7 to 9)
- Slides part 4 (covering sections 10 and 11)
- Slides part 5 (covering section 12)
- Slides part 6 (covering sections 13 and 14; section 15 to be added after Christmas)

Supplementary notes (non-examinable):

- 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 will appear here after homework deadlines.

Solutions released so far (up to question 51).

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

R Markdown example file

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

To contact the lecturer, email jonathan.jordan@sheffield.ac.uk.
My office is I9, on the fifth floor of the Hicks Building. I will have office hours **every Tuesday from 14:30 to 15:30**, but you can also try at other times if I am in.

A discussion board for this module is available on MOLE.

My home page

School of Mathematics and Statistics current students page

Last updated 18 January 2019.