Lecture 1 - Sample Space and events

Lecture 2 - Axioms of Probability

Lecture 3 - Independence of events and Conditional Probability

Lecture 4 - Baye’s Theorem and Introduction to Random Variables

Lecture 5 - CDF and it’s properties

Lecture 6 - Continuity of Probability

Lecture 7 - Discrete and Continuous random variables

Lecture 8 - Expectation of random variables and its properties

Lecture 9 - Variance and some inequalities of random variables

Lecture 10 - Discrete Probability Distributions

Lecture 11 - Continuous Probability Distributions

Lecture 12 - Jointly distributed random variables and conditional distributions

Lecture 13 - Correlation and Covariance

Lecture 14 - Transformation of random vectors

Lecture 15 - Gaussian random vector and joint Gaussian distribution

Lecture 16 - Random Processes

Lecture 17 - Properties of random Process

Lecture 18 - Poisson Process

Lecture 19 - Properties of Poisson Process - Part 1

Lecture 20 - Properties of Poisson Process - Part 2

Lecture 21 - Convergence of sequence of random variables - Part 1

Lecture 22 - Convergence of sequence of random variables - Part 2

Lecture 23 - Relation between different notions of convergence

Lecture 24 - Cauchy’s criteria of convergence

Lecture 25 - Convergence in expectation

Lecture 26 - Law of Large Numbers

Lecture 27 - Central limit theorem

Lecture 28 - Chernoff bound

Lecture 29 - Introduction to Markov property

Lecture 30 - Transition Probability Matrix

Lecture 31 - Finite dimensional distribution of Markov chains

Lecture 32 - Strong Markov Property

Lecture 33 - Stopping Time

Lecture 34 - Hitting Times and Recurrence

Lecture 35 - Mean Number of returns to a state

Lecture 36 - Communicating classes and class properties

Lecture 37 - Class Properties (Continued...)

Lecture 38 - Positive Recurrence and The Invariant Probability Vector

Lecture 39 - Properties of Invariant Probability Vector

Lecture 40 - Condition For Transience

Lecture 41 - Example of Queue

Lecture 42 - Queue Continued and Example of Page Rank

Lecture 43 - Introduction to renewal Theory

Lecture 44 - The Elementary Renewal Theorem

Lecture 45 - Application to DTMC

Lecture 46 - Renewal Reward Theorem

Lecture 47 - Introduction to Continuous Time Markov Chains

Lecture 48 - Properties of states in CTMC

Lecture 49 - Embedded markov chain