## E2 202 : Random Processes, Fall 2018## Lectures02 Aug 2018: Lecture-01 Preliminaries 07 Aug 2018: Lecture-02 Probability laws 09 Aug 2018: Lecture-03 Bayes’ Theorem and Independence of events 16 Aug 2018: Lecture-04 Random Variables 21 Aug 2018: Lecture-05 Random Vectors 23 Aug 2018: Lecture-06 Expectation 28 Aug 2018: Lecture-07 Generalized Expectations 30 Aug 2018: Lecture-08 Conditional Expectations 16 Oct 2018: Lecture-18 Random Processes: Independence 18 Oct 2018: Lecture-19 Tractable Random Processes 23 Oct 2018: Lecture-20 Introduction to Markov Chains 25 Oct 2018: Lecture-21 DTMC: Random Representation Mapping 27 Oct 2018: Lecture-22 DTMC: Strong Markov Property 30 Oct 2018: Lecture-23 DTMC: Hitting and Recurrence Times 01 Nov 2018: Lecture-24 DTMC: Irreducibility and Aperiodicity 06 Nov 2018: Lecture-25 DTMC: Invariant Distribution 13 Nov 2018: Lecture-26 Poisson point processes 15 Nov 2018: Lecture-27 Poisson point processes: Properties 20 Nov 2018: Lecture-28 Poisson processes on half-line 22 Nov 2018: Lecture-29 Poisson Processes: Compound and Non-stationary
## Homeworks17 Aug 2018: Homework 1 Solutions 31 Aug 2018: Homework 2 Solutions 28 Sep 2018: Homework 3 13 Oct 2018: Homework 4 Solutions 27 Oct 2018: Homework 5 Solutions 12 Nov 2018: Homework 6
## Tutorials
04 Aug 2018: Sample space, sigma algebra, example constructions of sigma algebras, “infinitely often” and “all but finitely many” events (Notes and exercises) 11 Aug 2018: Probability measure, continuity of probability, independence (Notes and exercises) 18 Aug 2018: Conditional probability, conditional independence (Notes and exercises) 22 Aug 2018: Borel sigma algebra, random variables, CDF and its properties, construction of CDF from a probability measure, example constructions of random variables with respect to various sigma algebras (Notes and exercises) 01 Sep 2018: Functions of random variables: sum, min, Jensen's inequality, Cauchy-Schwartz inequality (Notes and exercises) 08 Sep 2018: Sigma algebra generated by a random variable, Simulation of CDFs on a computer, properties of joint CDFs, overview of Riemann and Lebesgue integrals, independence of random variables - definition and equivalent forms for jointly discrete and jointly continuous random variables (Notes) (Exercises) 15 Sep 2018: Almost sure events, Markov's inequality, some properties of nonnegative random variables with finite expectation, self-independence of random variables (Notes and exercises) 20 Sep 2018: Problems (Notes and exercises) 29 Sep 2018: Transformations of RV ( Notes, Reference: Chapter 12 of this book). 06 Oct 2018: Conditional expectation, law of iterated expectations, geometric interpretation of conditional expectation as MMSE estimate, example problems (Notes and Exercises) 07 Oct 2018: Moment generating functions, characteristic functions, jointly Gaussian random variables (or Gaussian random vectors) (Notes and Exercises) 13 Oct 2018: Convergence of real sequences, modes of convergence of a sequence of random variables, Borel-Cantelli lemma, examples (Notes) 03 Nov 2018: Stopping times and basics of DTMCs (Notes) 08, 10 Nov 2018: Problems on hitting times, recurrence, invariant distributions (Notes)
## Tests01 Sep 2018: Quiz 1 Solution 15 Sep 2018: Quiz 2 Solution 22 Sep 2018: Mid Term 1 Solution 13 Oct 2018: Quiz 3 Solution 03 Nov 2018: Quiz 4 Solution 10 Nov 2018: Quiz 5 Solution 17 Nov 2018: Mid Term 2 24 Nov 2018: Quiz 6 06 Dec 2018: Final (Hours: 2pm - 5pm, Venue: EC 1.06,1.07,1.08)
## Grading PolicyMid Term 1: 15% ## Course Syllabus**Probability Theory:**axioms, continuity of probability, independence, conditional probability.**Random variables:**distribution, transformation, expectation, moment generating function, characteristic function**Random vectors:**joint distribution, conditional distribution, expectation, Gaussian random vectors.**Convergence of random sequences:**Borel-Cantelli Lemma, laws of large numbers, central limit theorem, Chernoff bound.**Discrete time random processes:**ergodicity, strong ergodic theorem, definition, stationarity, correlation functions in linear systems, power spectral density.**Structured random processes:**Bernoulli processes, independent increment processes, discrete time Markov chains, recurrence analysis, Foster's theorem, reversible Markov chains, the Poisson process.
## Course DescriptionBasic mathematical modeling is at the heart of engineering. In both electrical and computer engineering, uncertainty can be modeled by appropriate probabilistic objects. This foundational course will introduce students to basics of probability theory, random variables, and random sequences. ## Slack Information## SlackStudents can signup for course slack using their iisc.ac.in email at Slack signup. ## InstructorsUtpal Mukherji Parimal Parag ## Time and LocationClassroom: ECE 1.08, Main ECE Building. ## Teaching AssistantsKarthik P N Prathamesh Mayekar ## TextbooksProbability and Random Processes, Geoffrey Grimmett and David Stirzaker, 3rd edition, 2001. Discrete Event Stochastic Processes, Anurag Kumar, Department of Electrical Communication Engineering, Indian Institute of Science Random Processes for Engineers, Bruce Hajek, 2014. Introduction to Probability, Dimitri P. Bertsekas and John N. Tsitsiklis, 2nd edition, 2008. A First Course in Probability, Sheldon M. Ross, 2013. Probability Essentials, Jean Jacod & Philip Protter, Springer, 2004. Probability, Random processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance, Kobayashi, Hisashi, Brian L. Mark, and William Turin, Cambridge University Press, 2011. |