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 handouts and other material
Each lecture will be accompanied by a handout, all handouts will be
made available through this web site (below). The handouts cover the
material required, but they can be rather terse to read, so if you
prefer you can read up on the material using a textbook. There are a
large number of good textbooks, which cover the material needed. 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.
Lecture 1, Probability Fundamentals (handout)
[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 (handout)
[RHB pages: Permutations and Combinations: 1133-1135, Mean, Variance
and Moments: 1143-1148, Bionomial: 1168-1170, Poisson: 1174-1177]
Lecture 3, Continuous distributions (handout)
[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 (handout)
Lecture 5, Moment Generating Functions (handout)
[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 (handout)
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
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