# Introduction to Probability (with examples using R)

By Prof. Siva Athreya   |   Indian Statistical Institute
Learners enrolled: 1602
The course will cover basic concepts in Probability. It will begin with fundamental notions of Sample Space, Events, Probability, conditional probabilities And independence. We shall formalise notation in terms of Random Variables and discuss standard distributions such as (discrete) Uniform, Binomial, Poisson, Geometric, Hypergeometric, Negative Binomial and (continuous) Normal, Exponential, Gamma, Beta, Chi-square, and Cauchy. We will conclude with the law of large numbers and central limit theorem. A unique feature of this course will be that we will use the package R to illustrate examples.

INTENDED AUDIENCE
Anyone who has completed one year of undergraduate degree in Engineering or Sciences
PREREQUISITES : Basic Calculus
INDUSTRIES  SUPPORT     : None
Summary
 Course Status : Completed Course Type : Elective Duration : 12 weeks Category : Mathematics Foundations of Mathematics Credit Points : 3 Level : Undergraduate Start Date : 18 Jan 2021 End Date : 09 Apr 2021 Enrollment Ends : 01 Feb 2021 Exam Date : 25 Apr 2021 IST

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

### Course layout

Week 1:
* Sample Space, Events and Probability
* Conditional Probability and Independence
Week 2:
* Independence and Bernoulli Trials
* Poisson Approximation
Week 3:
* Sampling without Replacement
* Discrete Random Variables
Week 4:
* Discrete Random Variables:
o Distribution, Probability Mass function
o Joint, Marginal, and Conditional
o Independence
Week 5:
* Discrete Random Variables
o Expectation and Variance
o Correlation and Covariance
Week 6:
* Markov and Chebyschev Inequalties
* Conditional Expectation, Conditional Variance
Week 7:
* Uncountable Sample Spaces
* Probability Densities
* Continuous Random Variables: Uniform Distribution
Week 8:
* Exponential Random  and Normal Random Variable
* Joint Density, Marginal and Conditional Density
Week 9:
* Independence
* Functions of Random Variables
Week 10:
* Sums of Independent Random variables
* Distributions of Quotients of Independent Random variables.
Week 11:
* Law of Large Numbers (without Proof)
Week 12:
* Central Limit Theorem (without Proof)

### Books and references

https://www.isibang.ac.in/~athreya/psweur/

### 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: 25 April 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