Probability Part A
Hilary Term, 2012
First-lecture general information handout.
Other lecture notes: Here are Neil
Laws's lecture notes from Part A probability 3 years ago
The course is in four parts, each
taking up 2 weeks:
1. Joint distributions, expectation and conditioning
lecture notes Problem
sheet 1 (Sheet 1 updated 24/1. Mistake in question 6b
corrected.)
Lecture notes updated 30/1.
2. Generating functions, Limit laws of probability lecture
notes Problem sheet 2
You can download the cumulative first 8 chapters of lecture notes (which
cover what will likely be the first 9 lectures) with the link above.
The lecture notes for weeks 1 and 2 have been emended and slightly extended.
Slides for CLT
lecture (10 February)
3. Markov chains Problem sheet 3
4. Absorption probabilities, Recurrence, Poisson process
Sheet k includes material primarily from weeks 2k-1 and 2k, so should be
completely accessible
to those who have heard lecture 4k.
Specific comments on problem sheets:
(24/1) We should be through lecture 3 and the portion of lecture 4 required
for problem sheet 1 by the end of Friday 27/1.
Material for the following problems has not yet been covered in lectures:
Question 2b: section 4.6
Question 3c: section 4.4 (note: Example 2.7 could help for 3e; this is in
the new version of the lecture notes)
Question 6 depends on section 4.9 of the lecture notes, and we may not get
to it until next week
Question 7: section 3.4
Question 8: section 3.4, particularly the examples.
Other links
Applet
for calculating normal probabilities
Yuval Filmus's article
on proving the CLT with moments, including the proof of normal
distribution for number of prime factors.