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Introduction to Probability Theory and Stochastic Processes

By Prof. S Dharmaraja   |   IIT Delhi
Learners enrolled: 1093
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.
INTENDED AUDIENCE : 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.
Summary
Course Status : Completed
Course Type : Core
Duration : 12 weeks
Category :
  • Mathematics
  • Economics & Finance
Credit Points : 3
Level : Undergraduate
Start Date : 26 Jul 2021
End Date : 15 Oct 2021
Enrollment Ends : 09 Aug 2021
Exam Date : 23 Oct 2021 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.


Page Visits



Course layout

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

Books and references

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.

Instructor bio

Prof. S Dharmaraja

IIT Delhi
Prof. 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.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 23 October 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
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. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course. 
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

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 nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning. 

- NPTEL team


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