Core Overview:-
- Purpose: Explains natural, physical, and social phenomena governed by chance.
- Approach: Combines classical intuitive approaches with modern axiomatic probability.
- Target Audience: Designed for graduate-level students with a foundational background in mathematics.
According to publisher listings on Google Books and World Scientific, the curriculum balances pure mathematical definitions with extensive problem sets covering:
- Foundations of Probability: Axiomatic frameworks, classical definitions, and set theory bases.
- Univariate Distributions: Detailed analysis of single-variable probability functions.
- Multivariate Models: Covers bivariate normal distributions and multinomial distributions.
- Limits & Convergence: Evaluates how sequences of random variables converge under different modes.
- Unusual Probability Distributions: Explores specialized statistical distribution setups, including extensive work on power series distributions.
- Stochastic Processes: A preliminary introduction to random time-dependent phenomena.
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