Course materials
Weak I: Axiomatic definition of probability
Video Lectures:
Lecture I (review of probability) Notes used in lecture, handwritten notes
Lecture II (Axiomatic definition of probability) Notes used in lecture, handwritten notes
Lecture III(sigma fields and construction of probabilities on them) Notes used in lecture, handwritten notes
Weak II (Properties of sigma-field and probability)
Lecture IV (properties of probability) notes used in lecture handwritten notes
Reference: Rohatgi and Saleh
Tutorial on August 04, 2020: discussion notes
Lecture V (Conditional probability and independence) notes used in the lecture handwritten notes
List of exercises.
Week III (Introduction to random variables)
Lecture~6.0 (Preliminaries for the random variable) notes used in the lecture
Lecture~6 (Random variables) notes used in the lecture handwritten notes
Lecture~7 (Distribution function and its properties) notes used in the lecture handwritten notes
Please try to solve the exercises mentioned in the handwritten notes.
Week IV (Discrete and Continuous random variables and their properties)
Video lecture~8 (Discrete and continuous random variables) notes used in the lecture handwritten notes
Exercises (Please solve the exercises)
Video lecture~9 (Functions of random variables Part I) notes used in the lecture handwritten notes
Exercises (Please solve the exercises)
Special random variables with their p.m.f./p.d.f.
Week V (Moments, Quantiles and Generating Functions)
Video lecture 10: Functions of random variables: part II Notes used in the video lecture Handwritten lecture notes
Video lecture 10 (a): A complex example Notes used in the video lecture
Quiz 1: Question paper
Week VI (Quantiles and generating functions)
Lecture 11: introduction to quantiles and moments Notes used in video lecture handwritten lecture notes
Lecture 12: Formal introduction to moments Notes used in video lecture handwritten lecture notes
Exercises on Moments, quantiles and generating functions
Week VII (Moments and tail probabilities)
Lecture 13: Moment inequalities Notes used in the video lecture
Tutorial on 8th September (morning)
Tutorial on 8th September (evening)
Week VIII (Generating functions)
Lecture 14 Generating functions Lecture notes for video lecture
Lecture 15 Generating functions and moments Lecture notes for video lecture
Exercises on Moments and generating functions
Analytic exposition to generating functions for non-negative discrete random variables Lecture notes
Tutorial on 24th September Board work
Week IX (Classification of random vectors: joint, marginal and conditional distribution)
Video lecture 16: Introduction to random vectors Notes for the video lecture handwritten notes
Video lecture 17: marginal distributions, mass and density functions Notes for the video lecture handwritten notes
Video lecture 18: marginal distributions, mass and density functions: general framework Notes for video lecture
Video lecture 19: Conditional distributions part 1 Notes for the video lecture handwritten notes
Video lecture 20: conditional distributions and expectations part II Notes in video lecture
Week X (Independent random vectors and their functions)
Video lecture 21: Independent random variables and vectors notes used in video lecture handwritten notes
Video lecture 22 Lecture notes used in the video
Video lecture 23 Lecture notes used in the video Exercises for independent random variables and their moments
Lecture notes for Video lecture 24 : Moments of random vectors and functions of several random variables (Unfortunately there is no recording)
Video lecture 25: Functions of random vectors Notes for the video lecture handwritten notes
Video lecture 26: Functions of random vectors part II Notes for the video lecture
Exercises for functions of several random variables
Notes for the tutorial on October 27
Video lecture: Some exercises on moments of random vectors Notes used in the video lecture
Video lecture: Problem-solving session on functions of several random variables: part I Notes used in the lecture
Video lecture: Problem-solving session on functions of several random variables: part II Notes used in the lecture
Week XII (Convergence concepts I)
Video lecture on Convergence concepts of random variables Part I
Video lecture on Convergence concepts of random variables Part II
Video lecture on convergence concepts of random variables Part III
Notes used in the video lecture
Week XIII
Lecture video on Kolmogorov's consistency theorem and its consequences
Lecture video on the abstract construction of the random variables Notes used in the lecture
Video lecture asymptotics for the sum of IID Bernoulli random variables
Part V (Sum of independently (but not identically) distributed random variables)
Notes used in the lectures (Handwritten notes)
Probability inequalities based on moments (no video lectures as the handwritten notes are self-sufficient and we discussed them in detail for SLLN) handwritten notes
Probability Inequalities II handwritten notes Video lecture I Video lecture II
Lecture notes used in the video
Revisiting the definitions of convergences Handwritten lecture notes
Video lecture I Video lecture II
Lecture notes used in the video
Convergence concepts II
Video lecture I