# Introduction to Probability Theory and Stochastic Processes (Tamil)

- Institution: IIT Delhi
- Department: Mathematics
- Teacher: Prof. S Dharmaraja
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111102518)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111102518)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course explanations and expositions of probability and stochastic processes concepts which they need for their experiments and research. It also covers theoretical concepts of probability and stochastic processes pertaining to handling various stochastic modeling. This course provides random variable, distributions, moments, modes of convergences, classification and properties of stochastic processes, stationary processes, discrete and continuous time Markov chains and simple Markovian queueing models.

Intended audience: UG and research scholars

Prerequisites: Calculus or Mathematics 1

## Lectures

1. [Lecture 1 : Random Experiment, Sample Space and Sigma Field](https://invisiblenetwork.ai/learn/nptel/111102518/56ed630b83cd) (YouTube)
2. [Lecture 2 :Axiomatic Definition of Probability](https://invisiblenetwork.ai/learn/nptel/111102518/c68dee47feaa) (YouTube)
3. [Lecture 3 : Properties of Axiomatic Definition of Probability and Classical Definition of Probability](https://invisiblenetwork.ai/learn/nptel/111102518/cb54e8725b3c) (YouTube)
4. [Lecture 4 : Conditional Probability, Independent Events and Baye's Rule](https://invisiblenetwork.ai/learn/nptel/111102518/4fad0a6c4764) (YouTube)
5. [Lecture 5 : Definition of Random Variable](https://invisiblenetwork.ai/learn/nptel/111102518/5bfde8968d98) (YouTube)
6. [Lecture 6 : Cumulative Distribution Function](https://invisiblenetwork.ai/learn/nptel/111102518/e632e1d59a50) (YouTube)
7. [Lecture 7 : Discrete and Continuous Type Random Variables](https://invisiblenetwork.ai/learn/nptel/111102518/158119e83e15) (YouTube)
8. [Lecture 8 : Mixed Type Random Variable](https://invisiblenetwork.ai/learn/nptel/111102518/9044d6de2f0f) (YouTube)
9. [Lecture 9 : Function of a Random Variable](https://invisiblenetwork.ai/learn/nptel/111102518/21ad32790830) (YouTube)
10. [Lecture 10 : Mean](https://invisiblenetwork.ai/learn/nptel/111102518/4d94d150be40) (YouTube)
11. [Lecture 11 : Variance and higher order moments](https://invisiblenetwork.ai/learn/nptel/111102518/dea078c3a0b2) (YouTube)
12. [Lecture 12 : Inequalities of Markov and Chebyshev](https://invisiblenetwork.ai/learn/nptel/111102518/c3480cd94f1c) (YouTube)
13. [Lecture 13 : Generating functions](https://invisiblenetwork.ai/learn/nptel/111102518/5493e300ad9d) (YouTube)
14. [Lecture 14 : Standard discrete distributions](https://invisiblenetwork.ai/learn/nptel/111102518/5a2e5d96ae54) (YouTube)
15. [Lecture 15 : Standard discrete distributions (continued)](https://invisiblenetwork.ai/learn/nptel/111102518/64a71bdec7c6) (YouTube)
16. [Lecture 16 : Standard continuous distributions](https://invisiblenetwork.ai/learn/nptel/111102518/999cd6214654) (YouTube)
17. [Lecture 17 : Standard continuous distributions (continued)](https://invisiblenetwork.ai/learn/nptel/111102518/23ea3cb2a64f) (YouTube)
18. [Lecture 18 : Definition and Joint Distribution of a Random Vector](https://invisiblenetwork.ai/learn/nptel/111102518/89e3d4b4dd27) (YouTube)
19. [Lecture 19 : Joint Probability Mass Function](https://invisiblenetwork.ai/learn/nptel/111102518/e2e119bc708e) (YouTube)
20. [Lecture 20 : Joint Probability Density Function](https://invisiblenetwork.ai/learn/nptel/111102518/23d431f62789) (YouTube)
21. [Lecture 21 : Independent Random Vector](https://invisiblenetwork.ai/learn/nptel/111102518/71f1ff5c416a) (YouTube)
22. [Lecture 22 : Distribution of functions of random variables (Discrete type)](https://invisiblenetwork.ai/learn/nptel/111102518/377524fa302f) (YouTube)
23. [Lecture 23 : Distribution of functions of random variables (Continuous type)](https://invisiblenetwork.ai/learn/nptel/111102518/43157c07fd6d) (YouTube)
24. [Lecture 24 : Conditional Distribution of Random Variables (Discrete type)](https://invisiblenetwork.ai/learn/nptel/111102518/028c8fa74f73) (YouTube)
25. [Lecture 25 : Conditional Distribution of Random Variables (Continuous type)](https://invisiblenetwork.ai/learn/nptel/111102518/2220add2f41e) (YouTube)
26. [Lecture 26 : Expectation for several random variables](https://invisiblenetwork.ai/learn/nptel/111102518/88ea14d77459) (YouTube)
27. [Lecture 27 : Covariance and correlation coefficient](https://invisiblenetwork.ai/learn/nptel/111102518/9247b3839116) (YouTube)
28. [Lecture 28 : Generating functions for several random variables](https://invisiblenetwork.ai/learn/nptel/111102518/2991ee0380f5) (YouTube)
29. [Lecture 29 : Conditional Expectation](https://invisiblenetwork.ai/learn/nptel/111102518/d7944c9f88f0) (YouTube)
30. [Lecture 30 : Modes of convergence](https://invisiblenetwork.ai/learn/nptel/111102518/0e32fcb612b8) (YouTube)
31. [Lecture 31 : Modes of convergence (contd)](https://invisiblenetwork.ai/learn/nptel/111102518/d7577a7751bd) (YouTube)
32. [Lecture 32 : Law of Large Numbers](https://invisiblenetwork.ai/learn/nptel/111102518/c1d4fcbf60b2) (YouTube)
33. [Lecture 33 : Central Limit Theorem](https://invisiblenetwork.ai/learn/nptel/111102518/e4ded8f94648) (YouTube)
34. [Lecture 34 : Definition and Classification of Stochastic Processes](https://invisiblenetwork.ai/learn/nptel/111102518/657d6c1a17e8) (YouTube)
35. [Lecture 35 : Properties of Stochastic Processes](https://invisiblenetwork.ai/learn/nptel/111102518/0a9953f1510d) (YouTube)
36. [Lecture 36 : Properties of Stochastic Processes(Contd)](https://invisiblenetwork.ai/learn/nptel/111102518/9cbbb9270efd) (YouTube)
37. [Lecture 37 : Standard Simple Stochastic Processes](https://invisiblenetwork.ai/learn/nptel/111102518/fd7c967c1ef6) (YouTube)
38. [Lecture 38: Definition of Discrete Time Markov Chain (DTMC)](https://invisiblenetwork.ai/learn/nptel/111102518/8f29948d3bf6) (YouTube)
39. [Lecture 39: Chapman-Kolmogorov Equation](https://invisiblenetwork.ai/learn/nptel/111102518/4cb971970f13) (YouTube)
40. [Lecture 40: Classification of States](https://invisiblenetwork.ai/learn/nptel/111102518/a4e9c272aebc) (YouTube)
41. [Lecture 41 : Classification of States (Contd)](https://invisiblenetwork.ai/learn/nptel/111102518/a5e7cb3ebef3) (YouTube)
42. [Lecture 42 : Limiting Distribution](https://invisiblenetwork.ai/learn/nptel/111102518/c00489b13630) (YouTube)
43. [Lecture 43 : Stationary Distribution](https://invisiblenetwork.ai/learn/nptel/111102518/9401ee846495) (YouTube)
44. [Lecture 44 : Reducible Markov Chains](https://invisiblenetwork.ai/learn/nptel/111102518/88196dcee395) (YouTube)
45. [Lecture 45 : Definition of Continuous Time Markov Chain (CTMC)](https://invisiblenetwork.ai/learn/nptel/111102518/041e0d98b335) (YouTube)
46. [Lecture 46 : Infinitesimal Generator Matrix](https://invisiblenetwork.ai/learn/nptel/111102518/18522fdc03b3) (YouTube)
47. [Lecture 47 : Kolmogorov Differential Equations](https://invisiblenetwork.ai/learn/nptel/111102518/b9b265a83c06) (YouTube)
48. [Lecture 48 : Limiting Distribution and Steady-State Distribution](https://invisiblenetwork.ai/learn/nptel/111102518/56f8c721d9f8) (YouTube)
49. [Lecture 49 : Birth Death Processes](https://invisiblenetwork.ai/learn/nptel/111102518/c567c148b7de) (YouTube)
50. [Lecture 50 : Introduction to Queueing Models and Kendall Notation](https://invisiblenetwork.ai/learn/nptel/111102518/669ee5d9cc8f) (YouTube)
51. [Lecture 51 : Single-Server Queueing Models](https://invisiblenetwork.ai/learn/nptel/111102518/38f4073299ea) (YouTube)
52. [Lecture 52 : Single-Server Queueing Models (Contd)](https://invisiblenetwork.ai/learn/nptel/111102518/d4792e241d84) (YouTube)
53. [Lecture 53 : Multi-Server Queueing Models](https://invisiblenetwork.ai/learn/nptel/111102518/7a248bc5ac4d) (YouTube)