Courses » Introduction to Probability Theory and Stochastic Processes

Introduction to Probability Theory and Stochastic Processes


This course explanations and expositions of probability and stochastic processes concepts which they need for their experiments and research. It also covers theoretical concepts of probability and stochastic processes pertaining to handling various stochastic modeling. This course provides random variable, distributions, moments, modes of convergences, classification and properties of stochastic processes, stationary processes, discrete and continuous time Markov chains and simple Markovian queueing models.

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Final Exam (in-person, invigilated, currently conducted in India) is mandatory for Certification and has INR Rs. 1100 as exam fee.

Under-graduate students of electrical engineering, computer engineering, mechanical engineering, civil engineering and mathematics and computing



PREREQUISITES: A basic course on Calculus and Linear Algebra

INDUSTRY SUPPORT: Fractal Analytics, Genpact, Goldman Sachs, FinMechanics, Deutsche Bank and other finance companies.


S. Dharmaraja earned his M.Sc. degree in Applied Mathematics from Anna University, Madras, India, in 1994 and Ph.D. degree in Mathematics from the Indian Institute of Technology Madras, in 1999. From 1999 to 2002, he was a post-doctoral fellow at the Department of Electrical and Computer Engineering, Duke University, USA. From 2002 to 2003, he was a research associate at the TRLabs, Winnipeg, Canada. He has been with the Department of Mathematics, IIT Delhi, since 2003, where he is currently a Professor, Department of Mathematics and joint faculty of Bharti School of Telecommunication Technology and Management. During July 2014 and August 2017, he served as Head, Department of Mathematics. He appointed as 'Jaswinder & Tarvinder Chadha Chair Professor' for teaching and research in the area of Operations Research from May 2010 to July 2015. He has held visiting positions at the Duke University, USA, Emory University, USA, University of Calgary, Canada, University of Los Andes, Bogota, Colombia, National University of Colombia, Bogota, Colombia, University of Verona, Verona, Italy, Sungkyunkwan University, Suwon, Korea and Universita degli Studi di Salerno, Fisciano, Italy. His research interests include applied probability, queueing theory, stochastic modeling, performance analysis of computer and communication systems and financial mathematics. He has published over 45 papers in refereed international journals and over 20 papers in refereed international conferences in these areas. He is an Associate Editor of International Journal of Communication Systems and an Associate Editor of Opsearch. He is co-author of a text book entitled "Introduction to Probability and Stochastic Processes with Applications" in John Wiley (US Edition, New Jersey, June 2012) and (Asian Edition, New Delhi, Jan. 2016) and co-author of a text book entitled "Financial Mathematics: An Introduction" in Narosa, Nov. 2012.


Week 1  :  Basics of Probability
Week 2  :   Random Variable
Week 3  : Moments and Inequalities
Week 4  :  Standard Distributions
Week 5  :  Higher Dimensional Distributions
Week 6  :  Functions of Several Random Variables
Week 7  :  Cross Moments
Week 8  :  Limiting Distributions
Week 9  :  Introduction to Stochastic Processes (SPs)
Week 10  :  Discrete-time Markov Chains (DTMCs)
Week 11  :  Continuous-time Markov Chains (CTMCs)
Week 12  :  Simple Markovian Queueing Models


1. Liliana Blanco Castaneda, Viswanathan Arunachalam and S. Dharmaraja, Introduction to Probability and Stochastic Processes with Applications, Wiley, 2012
2. Kishor S. Trivedi, Probability, Statistics with Reliability, Queueing and Computer Science Applications, 2nd edition, Wiley, 2001.
3. Introduction to Probability Models, Sheldon M. Ross, Academic Press, tenth edition, 2009.  
  • The exam is optional for a fee.
  • Date and Time of Exam: October 28, 2018 (Sunday).
  • Time of Exams: Morning session 9am to 12 noon; Afternoon session: 2pm to 5pm.
  • Exam for this Course will be available in both morning & afternoon sessions.
  • Registration url: Announcements will be made when the registration form is open for registrations.
  • The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.


  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of  Best 8 out of 12 assignments
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras. It will be e-verifiable at http://nptel.ac.in/noc/