Probability foundations

Elementary probability notes

The purpose of this page is to collect material for a solid foundation in elementary probability. It consists of my University of Bristol Probability 1 Unit lecture slides, plus additional material that could not be included due to the lack of prerequisites or time.

The lecture slides
Combinations with repetitions
Measure theoretic definition of probability; continuity of probability; proper definition of random variables
Inclusion-exclusion for n events
Bernoulli LLN; Weierstrass approximation theorem
Poisson process
Negative Binomial, Hypergeometric distributions
The Normal density is normed
Stirling's formula, DeMoivre-Laplace local and global Central Limit Theorem
Joint continuous distributions; joint distribution transformations; Multivariate Normal; covariance matrix; proof of the continuous convolution formula
Continuous conditional distributions
Steiner's theorem and least squares
Joint moment generating functions
A few nice probability problems

Any comments are welcome!