Probability Theory Wiki article. Mathematica foundations of probability

Probability cheat sheet – webpage

–> Seeing theory -- a visual introduction to probability and statistics

Probability, Mathematical Statistics, Stochastic Processes – Probability Primer

http://cs.brown.edu/courses/cs242/lectures/

Probability space (wiki), based on Measure theory

Random variables

Basic results in probability theory

https://en.wikipedia.org/wiki/Chernoff_bound – https://en.wikipedia.org/wiki/Markov%27s_inequality

Probability distribution function

Discrete probability distributions

• Binomial distribution
• Multinomial distribution
• Poisson distribution
• Empirical distribution

Continuous probability distributions

• Normal distribution
• Student's t distribution
• Dirac delta
• Laplace distribution
• Gamma distribution
  • Exponential distribution
  • Erlang distribution
  • Chi-squared distribution. The distribution of the sum of squared Gaussian random variables.
• Beta distribution
• Pareto distribution (see Power laws)
• A broad family: Exponential family distributions

Joint probability distribution

• Multivariate Gaussian distribution
• Multivariate Student's t distribution
• Dirichlet distribution

Moments and cumulants

Generating functions

Central Limit Theorem

Transformation of random variables

Can be used for sampling from distributions given a uniform sampler!

Monte Carlo

Probabilistic Numerical methods for finding numerical answers to main questions in probability and elsewhere.

Accuracy, found by using the Standard error (see Statistical estimation!).

Combinatorics

Probabilistic method (see book)

Information theory

Information measures, like Entropy, Relative entropy, Mutual information

Baye's theorem, Bayesian statistics