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A complete textbook covering probability theory, generating functions, mathematical foundations, applications, and stochastic modelling.
Basic probability concepts, random variables, distributions, expectation, variance, and statistical foundations.
Discrete distributions, generating functions, probability generating functions, and common probability models.
PGF properties, moments, derivatives, independent sums, compound distributions, and mathematical theory.
Applications of PGFs in stochastic processes, modelling, reliability, queueing, and applied probability.
Advanced PGF methods, branching processes, stochastic models, and extended applications.
Advanced PGF theory, multivariate models, stochastic networks, computational methods, and modern applications.
This textbook is organised into chapters with interactive MDX content, mathematical explanations, worked examples, exercises, solutions, and references.