Lecture 30 (05/05/2022): Notes Video (Click the link above for lecture-notes)
Lecture 29 (04/05/2022): Notes Video (Click the link above for lecture-notes)
Lecture 28 (28/04/2022): Notes Video (Click the link above for lecture-notes)
Lecture 27 (26/04/2022): Notes Video
Lecture 26 (19/04/2022): Notes Video
Lecture 25 (12/04/2022): Notes Video
Content (Pages 236 - 244): Introduction to Dirichlet distribution using multivariate change of joint density formula, equality of distribution
Lecture 24 (06/04/2022): Notes Video
Content (Pages 227 - 235): Multinomial distribution, multivariate change of joint density formula (statement without proof), background of Dirichlet distribution
Lecture 23 (05/04/2022): Notes Video
Content (Pages 218 - 226): Further properties of correlation coefficient
Lecture 22 (31/03/2022): Notes Video
Content (Pages 209 - 217): Cauchy-Schwarz inequality with detailed analysis of equalities on both sides, definition of correlation coefficient and its symmetry
Lecture 21 (29/03/2022): Notes Video
Content (Pages 200 - 208): Construction of an L2 space as a quotient vector space and its probabilistic meaning
Lecture 20 (24/03/2022): Notes Video
Content (Pages 189 - 199): Properties of covariance and variance, computation of variance using bilinearity of covariance, examples
Lecture 19 (22/03/2022): Notes Video
Content (Pages 182 - 188): Properties and limitations of covariance and correlation coefficient, independence and uncorrelatedness, computation of covariance directly from the joint distribution, examples
Lecture 18 (17/03/2022): Notes Video
Content (Pages 173 - 181): Computation of variance and examples, introduction to covariance
Lecture 17 (15/03/2022): Notes Video
Content (Pages 164 - 172): Application of linearity of expectation to top-to-random shuffling, introduction to variance
Lecture 16 (11/03/2022): Notes Video
Content (Pages 158 - 163): Monotonicity of expectation
Lecture 15 (10/03/2020): Notes Video
Content (Pages 151 - 157): Linearity of expectation
Lecture 14 (08/03/2022): Notes Video
Content (Pages 140 - 150): Distribution of the polar coordinate transform of two iid standard normal random variables, Box-Muller method of simulation, formula for expectation of a real valued function of a random vector
Lecture 13 (03/03/2022): Notes Video
Content (Pages 132 - 139): Bivariate change of joint density formula (statement without proof) and its applications
Lecture 12 (01/03/2022): Notes Video
Content (Pages 121 - 131): Distribution of product of two jointly continuous random variables, towards bivariate change of joint density formula, open sets and path-connected sets in the two-dimensional real plane, Jacobian matrix
Lecture 11 (24/02/2022): Notes Video
Content (Pages 111 - 120): Examples of computations of a pdf of the ratio of two jointly continuous random variables, introduction to t and F distributions
Lecture 10 (22/02/2022): Notes Video
Content (Pages 101 - 110): Independence of k random variables, additivity of k independent gamma random variables, chi-squared distribution, distribution of ratio of two jointly continuous random variables
Lecture 09 (17/02/2022): Notes Video
Content (Pages 094 - 100): An important consequence of additivity of gamma distribution, a quick review of k-dimensional random vectors
Lecture 08 (15/02/2022): Notes Video
Content (Pages 081 - 093): Finding the distribution of a real valued function of a random vector, convolution formula, additivity of gamma distribution
Lecture 07 (10/02/2022): Notes Video
Content (Pages 067 - 080): Finding the distribution of a function of a random variable, change of density formula and applications
Lecture 06 (08/02/2022): Notes Video
Content (Pages 055 - 066): Calculation of pdf (if exists) from cdf and applications, computations for bivariate uniform distribution on the unit disk (The first half of Lecture 06 wasn't recorded by mistake - the students are requested to go through the detailed class-notes and ask questions in the next lecture if there is any doubt.)
Lecture 05 (03/02/2022): Notes Video
Content (Pages 044 - 054): Characterization of independence in the jointly continuous case, computations for independent random variables, examples of real valued functions of random vectors
Lecture 04 (01/02/2022): Notes Video
Content: (Pages 030 - 043): Computations for a bivariate pdf, independence of two random variables, characterization of independence in the discrete case
Lecture 03 (27/01/2022): Notes Video
Content (Pages 022 - 029): A brief overview of double integral as a repeated integral, continuous bivariate random vectors, joint pdf, marginal pdfs
Lecture 02 (25/01/2022): Notes Video
Content (Pages 008 - 021): Characterizing properties of a joint cdf, discrete bivariate random vectors, joint pmf, marginal pmfs, examples based on Polya's urn scheme and a simple drainage network model
Lecture 01 (20/01/2022): Notes Video
Content (Pages 001 - 007): Recap of discrete and continuous random variables, bivariate random vectors, joint cdf