Continuous-Time Markov Chains: Definitions and State Probabilities

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Covers examples of absorbing Markov chains in discrete time.

Explores discrete-time Markov chains, emphasizing first passage time probabilities and minimal solutions.

Explores birth and death chains, hitting probabilities, and expected game durations in Markov chains.

Discusses discrete-time Markov chains and absorption time in communication systems.

Explores the Bonus Malus system for insurance premiums and Markov chain transition probabilities.

Explores Markov chains' properties, expectations, and recurrence in Poisson processes.

Explores Markov chain games, hitting probabilities, and expected hitting times in a target set.

Covers the theory and applications of Markov chains in modeling random phenomena and decision-making under uncertainty.

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Explores probability inequalities, convergence types, and moment generating functions for distribution approximation.

Explores conditional density, expectations, and independence of random variables with practical examples.

Explores the statistical interpretation of entropy and disorder through calculating micro-state multiplicity in different configurations.

Explores conditional probability and Bayes' theorem, demonstrating their application in real-life scenarios.

Covers the Poisson process in detail, focusing on the probability law and its applications.

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