Probability Theory and Applications
Explore the fundamentals and advanced concepts of probability theory and its applications in this comprehensive 23-hour course. Delve into queuing models, Markov chains, stochastic processes, and reliability theory. Learn about birth and death processes, Little's formulae, and the strong law of large numbers. Study joint moment generating functions, reducible Markov chains, and Poisson processes. Examine the central limit theorem, random walks, and state classifications. Analyze various queuing models, including M/M/I, M/M/S, and M/M/I/K. Investigate convergence and limit theorems, transition probabilities, and time-reversible Markov chains. Explore reliability theory, including exponential and Weibull failure laws. Master discrete and continuous random variables, their distributions, and functions of random variables. Gain practical knowledge applicable to real-world scenarios in operations research, engineering, and data analysis.