Discrete and continuous random vectors, joint and marginal distributions, independence, linearity and monotonicity of expectation, covariance, variance of a sum, computations involving indicator random variables, examples.
Distributions of functions of random vectors, distributions of sums, products and quotients for bivariate continuous distributions.
Multinomial distribution, bivariate normal distribution and Dirichlet distribution.
Conditional distribution, conditional density, conditional expectation and variance, computations for a bivariate normal vector and other illustrations.
Discussion of almost sure convergence, convergence in probability and distribution. Markov’s inequality, Tchebyshev’s inequality and weak law of large numbers. Statements of central limit theorem and strong law of large numbers for i.i.d. random variables.
Sheldon Ross: A First Course in Probability (9th Edition)
W. Feller: Introduction to Probability: Theory and Applications - Vol. I and II
P. G. Hoel, S. C. Port and C. J. Stone: Introduction to Probability Theory
Wed and Fri, 2:00 PM - 4:10 PM
Lectures will be held on the Zoom platform. Lecture videos and notes will be uploaded here.
Problems will be given regularly in the lectures. The students will not have to submit the solutions. However, they are encouraged to solve them all, discuss the solutions with each other and also ask the teacher if there is any doubt. Problems similar to these will be given in the exams.
Evaluation will be carried out based on a mid-semester examination and a final examination with 50% weightage on each. The mode of these exams will be announced later.