** E2 202-O Random Process 3:1 (August 2022) **

**Course Instructor:** Aditya Gopalan, ECE

**Course description:** This course is a graduate-level course on probability and stochastic processes. It is assumed
that the students are familiar with multivariable calculus (functions of several variables, partial derivatives, integration in n-dimensional
real Euclidean spaces) and that they have some idea of elementary probability (e.g., as part of Foundations for Business Analytics of an undergraduate
course on mathematics). Some familiarity with vector spaces and matrices would be assumed. The course would be useful for first year Masters or Ph.D.
students and would equip them with basic background in probability which is required for more advanced courses such as Machine learning, Adaptive Signal
Processing etc. The course is a mathematics course, and the students are encouraged to solve many problems. There would be some tutorial classes to help
students with problem solving.

** Syllabus**

The axioms of probability theory, probability spaces, conditional probability, independence, random variables and distribution functions, continuous and discrete random variables, multiple random variables and joint distributions, conditional distributions, functions of random variables and random vectors, expectation and moments, conditional expectation, some moment inequalities, sequences of random variables and convergence concepts, laws of large numbers, sums of independent random variables and the central limit theorem, stochastic processes, stationarity and ergodicity, discrete time Markov chains, Poisson process, continuous time Markov chains, Brownian motion

** Textbooks / References**

- V. K. Rohatgi and A. K. M. E. Saleh, An Introduction to Probability and Statistics
- P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory
- P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Stochastic Processes
- S. M. Ross, Introduction to Probability Models

**Prerequisites: ** There are no formal prerequisites. However, students should be familiar with multivariate calculus.

** Grading: **

- Homework assignments (four) 40%
- Mid-term exam 30%
- Final exam 30%.