Lecture 1: Sample Space and events

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Lecture 2: Axioms of Probability

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Lecture 3: Independence of events and Conditional Probability

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Lecture 4: Baye's Theorem and Introduction to Random Variables

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Lecture 5: CDF and it's properties

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Lecture 6: Continuity of Probability

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Lecture 7: Discrete and Continuous random variables

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Lecture 8: Expectation of random variables and its properties

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Lecture 9: Variance and some inequalities of random variables

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Lecture 10: Discrete Probability Distributions

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Lecture 11: Continuous Probability Distributions

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Lecture 12: Jointly distributed random variables and conditional distributions

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Lecture 13: Correlation and Covariance

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Lecture 14: Transformation of random vectors

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Lecture 15: Gaussian random vector and joint Gaussian distribution

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Lecture 16: Random Processes

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Lecture 17: Properties of random Process

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Lecture 18: Poisson Process

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Lecture 19: Properties of Poisson Process (Part 1)

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Lecture 20: Properties of Poisson Process (Part 2)

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Lecture 21: Convergence of sequence of random variables (Part 1)

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Lecture 22: Convergence of sequence of random variables (Part 2)

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Lecture 23: Relation between different notions of convergence

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Lecture 24: Cauchy's criteria of convergence

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Lecture 25: Convergence in expectation

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Lecture 26: Law of Large Numbers

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Lecture 27: Central limit theorem

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Lecture 28: chernoff bound

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Lecture 29: Introduction to Markov property

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Lecture 30: Transition Probability Matrix

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Lecture 31: Finite dimensional distribution of Markov chains

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Lecture 32: Strong Markov Property

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Lecture 33: Stopping Time

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Lecture 34: Hitting Times and Recurrence

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Lecture 35: Mean Number of returns to a state

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Lecture 36: Communicating classes and class properties

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Lecture 37: Class Properties Continued

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Lecture 38: Positive Recurrence and The Invariant Probability Vector

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Lecture 39: Properties of Invariant Probability Vector

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Lecture 40: Condition For Transience

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Lecture 41: Example of Queue

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Lecture 42: Queue Continued and Example of Page Rank

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Lecture 43: Introduction to renewal Theory

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Lecture 44: The Elementary Renewal Theorem

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Lecture 45: Application to DTMC

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Lecture 46: Renewal Reward Theorem

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Lecture 47: Introduction to Continuous Time Markov Chains

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Lecture 48: Properties of states in CTMC

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Lecture 49: Embedded markov chain

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