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Advanced Topics in Probability and Random Processes

Advanced Topics in Probability and Random Processes. Instructor: Prof. P. K. Bora, Department of Electronics and Electrical Engineering, IIT Guwahati. The course will cover mainly two broad areas: (1) the concepts of the convergence a sequence of random variables leading to the explanation of important concepts like the laws of large numbers, central limit theorem; and (2) Markov chains that include the analysis of discrete and continuous time Markov Chains and their applications. (from nptel.ac.in)

Lecture 01 - Probability Basics


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Introduction to Probability and Random Variable
Lecture 01 - Probability Basics
Lecture 02 - Random Variable
Lecture 03 - Random Variable (cont.)
Random Process Basics and Infinite Sequence of Events
Lecture 04 - Random Vectors and Random Processes
Lecture 05 - Infinite Sequence of Events
Lecture 06 - Infinite Sequence of Events (cont.)
Convergence of a Sequence of Random Variables
Lecture 07 - Convergence of a Sequence of Random Variables
Lecture 08 - Weak Convergence
Lecture 09 - Weak Convergence (cont.)
Applications of Convergence Theory
Lecture 10 - Laws of Large Numbers
Lecture 11 - Central Limit Theorem
Lecture 12 - Large Deviation Theory
Markov Chain
Lecture 13 - Cramer's Theorem for Large Deviation
Lecture 14 - Introduction to Markov Processes
Discrete Time Markov Chain
Lecture 15 - Discrete Time Markov Chain 1
Lecture 16 - Discrete Time Markov Chain 2
Lecture 17 - Discrete Time Markov Chain 3
Lecture 18 - Discrete Time Markov Chain 4
Lecture 19 - Discrete Time Markov Chain 5
Continuous Time Markov Chain
Lecture 20 - Continuous Time Markov Chain 1
Lecture 21 - Continuous Time Markov Chain 2
Lecture 22 - Continuous Time Markov Chain 3
Martingale Process
Lecture 23 - Martingale Process
Lecture 24 - Martingale Process (cont.)