Part 1B Paper 7, Probability and Statistics

Background and Revision Material

These lectures will build on the foundations taught in part 1A mathematics. If you need to revise this material, follow this link for the notes and video lecture.

Lecture slides and other material

The slides used in the lectures will be made available through this web site (below), but they will not be distributed in hard copy at the lectures. If you prefer printed versions for note taking, you will have to print them yourself.

The slides cover all the material required, but they can be rather terse to read. If you prefer a longer text book style version, you have a number of posibilities:

Notes used in the 2015/16 season, written by Jossy Sayir are available through moodle. These notes are also divided into six lectures, and cover essentially the same material.
There are a large number of good textbooks, which cover the material needed. If you are already familiar with one of these, you can probably continue using it without any problems.
I recommend Riley, Hobson and Bence [RHB] 'Mathematical Methods for Physics and Engineering' (CUP, 3rd edition), parts of chapter 30 'Probability' and chapter 31 'Statistics' -- some of you know this book already, it is short, clear and to the point. The lectures won't adhere tightly to the chapters, but I'll indicate below the approximate page numbers relevant to each of the 6 lectures

Note: inconsistency of notation

Unfortunately, there is an inconsistency in the definition of the concept of Moment Generating Function (MGF) for continuous probability distibutions. In the past (upto and including including 2015/16) the definition used in the notes for this module and in the mathematics databook, differed from the definition used by most of the rest of the world by including a negative sign. There is no really "correct" or "incorrect" definition, it is just a question of convention. We have now changed our convention (in the module slides and in the new version of the databook) to be more in line with the rest of the world. However, please be careful if you use older slides, past exam questions, etc. I will do my best to point out when we get to that material. I apologise for this extra confusion.

Lecture 1, Probability Fundamentals (slides)

[RHB pages: Venn Diagrams and Probability: 1119-1133, Discrete Random Variable: 1139-1140, Sample Mean and Variance: 1221-1224]

Wikipedia entry for entropy

Lecture 2, Discrete probability distributions (slides)

[RHB pages: Permutations and Combinations: 1133-1135, Mean, Variance and Moments: 1143-1148, Bionomial: 1168-1170, Poisson: 1174-1177]

Lecture 3, Continuous distributions (slides)

[RHB pages: Continuous distributions: 1140-1142, Mean: 1143-1145, Variance: 1146, Gaussian: 1179-1185, Exponential: 1190-1191]

The Beta distribution isn't covered in RHB, see eg the wikipedia entry if you want to know more.

Lecture 4, Combining and manipulating distributions (slides)

Lecture 5, Moment Generating Functions (slides)

[RHB pages: Note the slight inconsistency in naming: what in the course notes are referred to as Moment Generating Functions, are in RHB called Probability Generating Functions for discrete distributions and Moment Generating Functions for continuous ones. Probability Generating Functions: 1157-1161, Moment Generating Functions: 1162-1164, multivariate Gaussian: 1209-1210, Central Limit Theorem: 1195]

Lecture 6, Testing and statistical significance (slides)

The advanced material concerning model B on slides 12-14 of lecture 6 is good to know about, but you will not be expected to be able to derive this at the exam.

[RHB pages: Hypothesis testing: 1277-1280]

Examples Papers

Two example classes are scheduled: Feb 15th at 11:00-12:00 in lecture room 3A and March 8th at 11:00-12:00 in lecture room 3A.

Examples paper number 7/5
Examples paper number 7/6

The questions on the examples papers are roughly alligned with the material covered in the lectures. You should be able to attempt the questions as follows:
lect 1: paper 7/5: Q1, Q2, Q3, Q5
lect 2: paper 7/5: Q6, Q7, Q8
lect 3: paper 7/5: Q4, Q9 and paper 7/6: Q1
lect 4: paper 7/6: Q2, Q3
lect 5: paper 7/6: Q4, Q5, Q6
lect 6: paper 7/6: Q7

Lecturer

Carl Edward Rasmussen