Applied Probability & Stochastic Processes

This lecture covers the fundamental concepts of applied probability and stochastic processes, focusing on topics such as transition probability matrices, Markov chains, and characteristic polynomials. The instructor explains the n-step transition probability matrix, eigenvalues, and linear combinations of matrices. The lecture also delves into communication classes, recurrent and transient states, and the Cayley-Hamilton theorem. Various exercises explore random walks, invariant distributions, and expected return times in different scenarios.