NPTEL : NOC:Introduction to Probability (with examples using R) (Mathematics)

Co-ordinators : Prof. Siva Athreya


Lecture 1 - Sample Space, Events and Probability

Lecture 2 - Properties of Probability

Lecture 3 - Equally likely Outcomes

Lecture 4 - Conditional Probability

Lecture 5 - Bayes Theorem

Lecture 6 - Independence - Part 1

Lecture 7 - Independence - Part 2

Lecture 8 - Sampling and Repeated Trials

Lecture 9 - Sampling and Repeated Trials - Part 1

Lecture 10 - Sampling and Repeated Trials - Part 2

Lecture 11 - Sampling with and Without Replacement

Lecture 12 - Sampling without Replacement

Lecture 13 - Hypergeometric Distribution and Discrete Random Variables

Lecture 14 - Discrete Random Variables - Part 1

Lecture 15 - Discrete Random Variables - Part 2

Lecture 16 - Conditional, Joint and Marginal Distributions

Lecture 17 - Memoryless property of Geometric Distribution

Lecture 18 - Functions of Random Variables

Lecture 19 - Sums of Independent Random Variables

Lecture 20 - Functions and Independence

Lecture 21 - Expectation of Random Variables

Lecture 22 - Properties of Expectation

Lecture 23 - Expectation: Independence and Functions

Lecture 24 - Variance of Discrete Random Variables

Lecture 25 - Markov and Chebyshev Inequalities

Lecture 26 - Conditional Expectation and Covariance

Lecture 27 - Continuous Random Variables - Part 1

Lecture 28 - Continuous Random Variables - Part 2

Lecture 29 - Distribution Function

Lecture 30 - Exponential and Normal Random Variable

Lecture 31 - Normal Random Variable

Lecture 32 - Change of Variable

Lecture 33 - Joint Distribution of Continuous Random Variables

Lecture 34 - Marginal Density and Independence

Lecture 35 - Conditional Density

Lecture 36 - Sums of Independent Random Variables

Lecture 37 - Quotient of Independent Random Variables

Lecture 38 - Expectation and Variance of Continuous Random Variables

Lecture 39 - Sampling Distribution and Sample Mean

Lecture 40 - Weak Law of Large Numbers

Lecture 41 - Revisit of Variance and Expectation

Lecture 42 - Revisit of Properties of Variance

Lecture 43 - Revisit Weak Law of Large Numbers

Lecture 44 - Demoivre-Laplace Central Limit Theorem and Normal Random Variables

Lecture 45 - Revisit Normal Random Variables

Lecture 46 - Normal Tables, Mean and Variance