Lecture 1 - Introduction to Probability
Lecture 2 - Conditional Probability
Lecture 3 - Total Probability and Bayes’ Rule
Lecture 4 - Random Variables (Discrete)
Lecture 5 - Discrete Random Variables and Special Distributions
Lecture 6 - Continuous Random Variables
Lecture 7 - Expectation, Variance and Joint Distributions
Lecture 8 - Conditional pmfs and pdfs, Independence
Lecture 9 - Conditional Expectation and Conditional Variance
Lecture 10 - Functions of random variable, sampling, limit theorems
Lecture 11 - Introduction to Stochastic Processes, Hitting Time
Lecture 12 - Markov Chains
Lecture 13 - Chapman-Kolmogorov Equations
Lecture 14 - Classification of States
Lecture 15 - Limiting and Stationary Distributions
Lecture 16 - Existence and Uniqueness of Stationary Distributions
Lecture 17 - Positive and Null Recurrence
Lecture 18 - Computation of Stationary Distribution and Gambler's Ruin
Lecture 19 - Mean Time in Transient States and Branching Processes
Lecture 20 - Hidden Markov Models
Lecture 21 - Introduction to counting processes and Bernoulli random processes
Lecture 22 - Foundations of discrete-time Bernoulli random processes
Lecture 23 - Bernoulli random processes: Alternate synthesis approaches
Lecture 24 - Counting function of Bernoulli random processes
Lecture 25 - Operations on Bernoulli random processes, and summary
Lecture 26 - Foundations of continuous-time Poisson random processes
Lecture 27 - Poisson counting processes: Dynamical system approach, counting function
Lecture 28 - Bernoulli approximation of Poisson processes, Key properties and illustrations via counting functions of Poisson counting processes
Lecture 29 - Operations on Poisson counting processes, Illustrative examples
Lecture 30 - Illustrative examples involving Poisson counting processes, summary, and comparison of Bernoulli and Poisson counting processes
Lecture 31 - Continuous-time Markov Chains (CTMCs): Introduction
Lecture 32 - CTMCs Foundations 1: Formal definitions of important quantities associated with CTMCs
Lecture 33 - CTMCs Foundations 2: Transition rates, Generator, Embedded chains
Lecture 34 - CTMCs via a sequence of DTMCs
Lecture 35 - Birth-Death CTMCs: Foundations
Lecture 36 - Birth-Death CTMCs: Illustrations
Lecture 37 - CTMCs: A re-look using first principles approach - I
Lecture 38 - CTMCs: A re-look using first principles approach - II
Lecture 39 - Transient analysis of CTMCs
Lecture 40 - Steady state analysis of CTMCs, Reversibility, birth-death chains and reversibility
Lecture 41 - Renewal process: Foundations, examples, applications
Lecture 42 - Counting function of Renewal processes
Lecture 43 - Renewal function and Elementary renewal theorem
Lecture 44 - CLT for Renewal processes, Renewal reward theorem, Illustration via age of renewal
Lecture 45 - Renewal process: Illustrations and extensions
Lecture 46 - Queuing theory: Foundations, applications, Illustrative example via timing diagram
Lecture 47 - Discrete-time Queues: Geo/Geo/1 queues
Lecture 48 - Continuous-time Queues: M/M/* queues
Lecture 49 - Delay models and delay analysis in Queueing theory
Lecture 50 - Queueing Theory: General queues, Burke's theorem, Tandem queues, examples
Lecture 51 - Introduction to Brownian Motion and Random Walks
Lecture 52 - Properties and Joint Distributions of Brownian Motion
Lecture 53 - White Noise and Stochastic Integrals
Lecture 54 - Gaussian Processes and Brownian Bridge
Lecture 55 - Stationary Processes and Random Telegraph Signal
Lecture 56 - Second-Order Stationarity and Auto-Regressive Processes
Lecture 57 - Linear Systems and Spectral Density
Lecture 58 - Pricing Stock Options and Arbitrage Theorem
Lecture 59 - Martingales and Geometric Brownian Motion
Lecture 60 - Black-Scholes Formula and Jump Processes
