Review some mathematical tools that are frequently used in probability theory and statistics.

The basics of sets and set operations (union, intersection, complement)

Generalizing the concept of permutation, counting k-permutations

Ordering objects, counting permutations, the factorial function

Subdividing objects into groups, counting the number of possible subdivisions

Choosing groups of objects, counting them, the binomial coefficient

Convergence, convergence criteria, metrics

Definition of sequence, countable and uncountable sets

Definite and indefinite integrals, computation rules

Review of differentiation rules

The basic rules used to compute the derivative of a function

A short course on the fundamentals of matrix algebra

A ratio of Gamma functions

A generalization of the factorial function

The book

Most learning materials found on this website are now available in a traditional textbook format.

Featured pages

- Convergence in distribution
- Mean square convergence
- Multivariate normal distribution
- Wishart distribution
- Set estimation
- Moment generating function

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Main sections

- Mathematical tools
- Fundamentals of probability
- Probability distributions
- Asymptotic theory
- Fundamentals of statistics
- Glossary

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Glossary entries

- Posterior probability
- Factorial
- Integrable variable
- Precision matrix
- Type I error
- Probability mass function

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