[HD] High Quality Summarised Study Notes for STAT3021

Description

I finished the unit in 2022 semester 1, so the content should not have changed much. Contents covered in the notes include: Week 01: Preliminaries: moment generating function, joint distribution, conditional probability and conditional expectation, random sum and basic concepts of stochastic processes Week 02: Markov chain: transition probabilities, Chapman-Kolmogorov equations, and classification of states Week 03: Markov Chain: Periodicity, recurrence and transience, positive and null recurrences Week 04: Markov Chain: limit distribution, stationary distribution, absorption probability and mean return time Week 05: Random walk and Branching processes: Gambler's ruin problem, expected duration, extinction probability Week 06: Random walk and Branching processes: expected duration, extinction probability Week 07: Basic properties of Poisson distribution and exponential distribution Week 08: Poisson processes: definition, interarrival and arrival (waiting) times, conditional distribution of arrival time Week 09: Poisson processes: splitting and merging a Poisson process, non-homogeneous Poisson process and compound Poisson process Week 10: Continuous-time Markov chains: definition and basic properties, the Embedded Markov Chain and the generator matrix, forward and backward Equations, stationary and limit distributions Week 11: Simple queuing theory: the M/M/1 queue, the M/M/1 queue with finite capacity and the M/M/k queue Week 12: Introduction to BM and martingale