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Course11110216058 lectures

Introduction to Probability Theory and Statistics

Prof. S Dharmaraja · IIT Delhi

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Lecture 1 Video
  2. Random experiment, sample space, axioms of probability, probability space. (Cont...) Video
  3. Random experiment, sample space, axioms of probability, probability space. (Contd...) Video
  4. Conditional probability, independence of events. Video
  5. Multiplication rule, total probability rule, Bayes's theorem. Video

week-02

  1. Lecture 6 Video
  2. Definition of Random Variable, Cumulative Distribution Function (Continued 1) Video
  3. Definition of Random Variable, Cumulative Distribution Function (Continued 2) Video
  4. Type of Random Variables, Probability Mass Function, Probability Density Function Video
  5. Type of Random Variables, Probability Mass Function, Probability Density Function (continued 1) Video
  6. Distribution of Function of Random Variables Video

week-03

  1. Lecture 12 Video
  2. Mean and Variance Continued Video
  3. Higher Order Moments and Moments Inequalities Video
  4. Higher Order Moments and Moments Inequalities Continued Video
  5. Generating Functions Video
  6. Generating Functions Continued Video

week-04

  1. Lecture 18 Video
  2. Common Discrete Distributions Continued Video
  3. Common Continuous Distributions Video
  4. Common Continuous Distributions Continued Video
  5. Applications of Random Variable Video
  6. Applications of Random Variable Continued Video

week-05

  1. Lecture 24 Video
  2. Joint probability mass function Video
  3. Joint probability density function Video
  4. Independent random variables Video
  5. Independent random variables Continued Video

week-06

  1. Lecture 29 Video
  2. Functions of several random variables continued Video
  3. Some important results Video
  4. Order statistics Video
  5. Conditional distributions Video
  6. Random sum Video

week-07

  1. Lecture 35 Video
  2. Variance Covariance matrix Video
  3. Multivariate Normal distribution Video
  4. Probability generating function and Moment generating function Video
  5. Correlation coefficient Video
  6. Conditional Expectation Video
  7. Conditional Expectation continued. Video

week-08

  1. Lecture 42 Video
  2. Mode of Convergence (Continued) Video
  3. Law of Large Numbers Video
  4. Central Limit Theorem Video
  5. Central Limit Theorem (Continued) Video

week-09

  1. Lecture 47 Video
  2. Lecture 48 Video
  3. Lecture 49 Video

week-10

  1. Lecture 50 Video
  2. Lecture 51 Video
  3. Lecture 52 Video

week-11

  1. Lecture 53 Video
  2. Lecture 54 Video
  3. Lecture 55 Video

week-12

  1. Lecture 56 Video
  2. Lecture 57 Video
  3. Lecture 58 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Delhi
Department
Mathematics
Teacher
Prof. S Dharmaraja
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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