Swayam Central

# Introduction to Stochastic Processes

By Prof. Manjesh hanawal   |   IIT Bombay
Randomness is a common thing that we came across in our daily life. Questions like how much traffic will be on my route today? how much I need to wait to catch a bus to my workplace? will I gain or lose money in stock market? may not have fixed answers as they are associated with events that are not in our control and could be treated as random. In this course, we will learn various probability techniques to model random events and study how to analyze their effect.

INTENDED AUDIENCE : All disciplines learners
PRE-REQUISITE : Introductory real analysis
SUPPORT INDUSTRY : This is a basic course. All companies will recognize

Learners enrolled: 697

### SUMMARY

 Course Status : Ongoing Course Type : Elective Duration : 12 weeks Start Date : 27 Jan 2020 End Date : 17 Apr 2020 Exam Date : 25 Apr 2020 Enrollment Ends : 03 Feb 2020 Category : Management Studies Level : Postgraduate
This is an AICTE approved FDP course

### COURSE LAYOUT

Week 1: Introductions to events, probability, conditional probability, Bayes rule
Week 2: Random Varaibles, Expectations, Variance, Various type of distributions
Week 3: CDF and PDF of random variables. Conditional CDF and PDFs
Week 4: Jointly distributed random variables, covariance and independence
Week 5: Transformation of random variables and their distributions
Week 6: Introductions to Random processes. Stationary and Ergodicity
Week 7: Convergence of Sequence of RVs. (almost surely, in probability, in distributions).
Week 8: Strong and weak law of large numbers, central limit theorem
Week 9: Discrete Markov chains. Stopping time and Strong Markov property Classification of Transient and Recurrent states
Week 10: Counting Process, Poisson Processes and its applications
Week 11: Renewal Theory. Elementary and Renewal Reward Theorem and
Week 12: Introduction to Continuous Markov Chains

### BOOKS AND REFERENCES

1) Introduction to Probability Models by Sheldon Ross
2) Random Process for Engineers by Bruce Hajek

### Prof. Manjesh hanawal

IIT Bombay
Manjesh K. Hanawal received the M.S. degree in ECE from the Indian Institute of Science, Bangalore, India, in 2009, and the Ph.D. degree from INRIA, Sophia Antipolis, France, and the University of Avignon, Avignon, France, in 2013. After two years of postdoc at Boston University, he is now an Assistant Professor in Industrial Engineering and Operations Research at the Indian Institute of Technology Bombay, Mumbai, India. His research interests include performance evaluation, machine learning and network economics. He is a recipient of Inspire Faculty Award from DST and Early Career Research Award from SERB

### 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: 25th April 2020, 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 Bombay. It will be e-verifiable at nptel.ac.in/noc.
• Only the e-certificate will be made available. Hard copies will not be dispatched.