Introduction to probability theory and random process.
Markov Chains: Transistion Probability Matrices. Classification of States, Recurrence; Basic Limit Theorems. Discrete Renewal Equation, absorption Probabilities, Criteria for recurrence.
Some Queuing Models (M/G/1, G/M/1), Random Walk: Continuous Time Markov Chains : Birth process, Birth & Death processes, Differential Equations of Birth & Death Processes, Absorption.
Renewal Processes: Renewal Equations, Elementary renewal Theorem, Renewal Theorem and Applications. Generalizations and variations.
Martingales : Supermartingales and Submartingales, Optional Sampling Theorem, Martingale conveyance Theorems.