Probability –II with Examples Using R

By Prof. Siva Athreya | Indian Statistical Institute

Learners enrolled: 463

ABOUT THE COURSE:
The course is part-2 of the two part Probability course. It will begin with a review of probability densities on the real line, and then discuss Bivariate continuous distributions including the Bivariate normal distribution. Then we will compute distribution of sums and quotients of continuous random variables. Expectation/mean, moments, variance, and conditional expectation will be understood for continuous random variables. It will conclude by proving Weak law of large numbers using Tchebyshev’s inequality and a discussion of the strong law of large numbers and Central Limit Theorm. We will use the package R to illustrate examples and give exercises.

INTENDED AUDIENCE: Undergraduate students

PREREQUISITES: Class XII Mathematics

INDUSTRY SUPPORT: Data Science companies

Summary

Course Status :	Completed
Course Type :	Core
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Undergraduate
Start Date :	25 Jul 2022
End Date :	14 Oct 2022
Enrollment Ends :	08 Aug 2022
Exam Date :	29 Oct 2022 IST

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

Page Visits

Course layout

1. Review of continuous random variables and probability densities on the real line,

2. Bivariate continuous distributions, bivariate cummulative distribution functions. Independence and marginal distributions.Conditional distribution, conditional density. E.g. : Bivariate Dirichlet and Normal Distributions

3. Distributions of sums and quotients for continuous distributions.

4. Expectation, variance and moments of random variables. Conditional expectation and variance.

5. Moment generating functions. Markov’s inequality, Tchebyshev’s inequality

6. Discussion of convergence with probability one, convergence in probability and distribution. Weak law of large numbers. State- ments of CLT and Strong law of large numbers for i.i.d. random variables.

Books and references

Probability and Statistics with Examples Using Rhttps://www.isibang.ac.in/~athreya/psweur/

Instructor bio

Prof. Siva Athreya

Indian Statistical Institute

Siva Athreya, is a Professor at the Indian Statistical Institute, Bangalore. He works in the area of Probability theory. He teaches in the B.Math (hons.), M.Math and Ph.d programs.

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: October 29, 2022 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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