Probability is a way of determining how likely something is to happen, and the area of math called probability theory gives us the mathematical tools necessary to analyze each situation and perform the necessary calculations. Probability is used extensively in statistics, finance, gambling, science, and philosophy.
A rigorous course in probability will cover many of the topics listed below:
- The need for measure theory
- Probability triples
- Probabilistic foundations
- Expected values
- Inequalities and convergence
- Distributions of random variables
- Stochastic processes and gambling games
- Discrete Markov chains
- Probability theorems
- Weak convergence
- Characteristic functions
- Decomposition of probability laws
- Conditional probability and expectation
- General stochastic processes
A large number of good books on probability can be found, a good place to start being Amazon.com. In addition, there is an excellent probability tutorial at West Texas A&M University.
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