# Probability Theory and Applications

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Prabha Sharma
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104079)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104079)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture-01-Basic principles of counting](https://invisiblenetwork.ai/learn/nptel/111104079/c1ef5ba12efc) (Video)
2. [Lecture-02-Sample space , events, axioms of probability](https://invisiblenetwork.ai/learn/nptel/111104079/84a8d7e683f3) (Video)
3. [Lecture-03-Conditional probability, Independence of events.](https://invisiblenetwork.ai/learn/nptel/111104079/8133df0cc81a) (Video)
4. [Lecture-04-Random variables, cumulative density function, expected value](https://invisiblenetwork.ai/learn/nptel/111104079/a4a0bd116261) (Video)
5. [Lecture-05-Discrete random variables and their distributions](https://invisiblenetwork.ai/learn/nptel/111104079/4dfd7564301e) (Video)
6. [Lecture-06-Discrete random variables and their distributions](https://invisiblenetwork.ai/learn/nptel/111104079/a9599a206b04) (Video)
7. [Lecture-07-Discrete random variables and their distributions](https://invisiblenetwork.ai/learn/nptel/111104079/3a19315fb14f) (Video)
8. [Lecture-08-Continuous random variables and their distributions.](https://invisiblenetwork.ai/learn/nptel/111104079/5a8d222cdc68) (Video)
9. [Lecture-09-Continuous random variables and their distributions.](https://invisiblenetwork.ai/learn/nptel/111104079/dc43e25b172d) (Video)
10. [Lecture-10-Continuous random variables and their distributions.](https://invisiblenetwork.ai/learn/nptel/111104079/d13ab12a1b28) (Video)
11. [Lecture-11-Function of random variables, Momement generating function](https://invisiblenetwork.ai/learn/nptel/111104079/680469720af2) (Video)
12. [Lecture-12-Jointly distributed random variables, Independent r. v. and their sums](https://invisiblenetwork.ai/learn/nptel/111104079/a2dd20c7301d) (Video)
13. [Lecture-13-Independent r. v. and their sums.](https://invisiblenetwork.ai/learn/nptel/111104079/9cca14a87384) (Video)
14. [Lecture-14-Chi – square r. v., sums of independent normal r. v., Conditional distr.](https://invisiblenetwork.ai/learn/nptel/111104079/eb21afd8e5fe) (Video)
15. [Lecture-15 Conditional disti, Joint distr. of functions of r. v., Order statistics](https://invisiblenetwork.ai/learn/nptel/111104079/6f1e714bb904) (Video)
16. [Lecture-16-Order statistics, Covariance and correlation.](https://invisiblenetwork.ai/learn/nptel/111104079/a4c4099beb55) (Video)
17. [Lecture-17-Covariance, Correlation, Cauchy- Schwarz inequalities, Conditional expectation.](https://invisiblenetwork.ai/learn/nptel/111104079/8cb352331d3d) (Video)
18. [Lecture-18-Conditional expectation, Best linear predictor](https://invisiblenetwork.ai/learn/nptel/111104079/9a9d920f08e3) (Video)
19. [Lecture-19-Inequalities and bounds.](https://invisiblenetwork.ai/learn/nptel/111104079/e00167ca1377) (Video)
20. [Lecture-20-Convergence and limit theorems](https://invisiblenetwork.ai/learn/nptel/111104079/9f67bcc4b604) (Video)
21. [Lecture-21-Central limit theorem](https://invisiblenetwork.ai/learn/nptel/111104079/ad38853e1619) (Video)
22. [Lecture-22-Applications of central limit theorem](https://invisiblenetwork.ai/learn/nptel/111104079/32a13f975a91) (Video)
23. [Lecture-23-Strong law of large numbers, Joint mgf.](https://invisiblenetwork.ai/learn/nptel/111104079/0999db612cda) (Video)
24. [Lecture-24-Convolutions](https://invisiblenetwork.ai/learn/nptel/111104079/b80f2bad7e1e) (Video)
25. [Lecture-25-Stochastic processes: Markov process.](https://invisiblenetwork.ai/learn/nptel/111104079/6bb5feba4552) (Video)
26. [Lecture-26-Transition and state probabilities.](https://invisiblenetwork.ai/learn/nptel/111104079/d9e21ef0a130) (Video)
27. [Lecture-27-State prob., First passage and First return prob](https://invisiblenetwork.ai/learn/nptel/111104079/2ee7a9cb51e6) (Video)
28. [Lecture-28-First passage and First return prob. Classification of states.](https://invisiblenetwork.ai/learn/nptel/111104079/3d12da3cad2c) (Video)
29. [Lecture-29-Random walk, periodic and null states.](https://invisiblenetwork.ai/learn/nptel/111104079/ad78a831a678) (Video)
30. [Lecture-30-Reducible Markov chains](https://invisiblenetwork.ai/learn/nptel/111104079/2ec9868e8051) (Video)
31. [Lecture-31-Time reversible Markov chains](https://invisiblenetwork.ai/learn/nptel/111104079/a7562aa19480) (Video)
32. [Lecture-32-Poisson Processes](https://invisiblenetwork.ai/learn/nptel/111104079/6ba39004c478) (Video)
33. [Lecture-33-Inter-arrival times, Properties of Poisson processes](https://invisiblenetwork.ai/learn/nptel/111104079/a092e0bb5d1c) (Video)
34. [Lecture-34-Queuing Models: M/M/I, Birth and death process, Little’s formulae](https://invisiblenetwork.ai/learn/nptel/111104079/2d37490283d1) (Video)
35. [Lecture-35-Analysis of L, Lq ,W and Wq , M/M/S model](https://invisiblenetwork.ai/learn/nptel/111104079/90389a10db1d) (Video)
36. [Lecture-36-M/M/S , M/M/I/K models](https://invisiblenetwork.ai/learn/nptel/111104079/925a2efc9b89) (Video)
37. [Lecture-37-M/M/I/K and M/M/S/K models](https://invisiblenetwork.ai/learn/nptel/111104079/b608df334ed2) (Video)
38. [Lecture-38-Application to reliability theory failure law](https://invisiblenetwork.ai/learn/nptel/111104079/55e7dbe541c2) (Video)
39. [Lecture-39-Exponential failure law, Weibull law](https://invisiblenetwork.ai/learn/nptel/111104079/75b9b7d1b2d9) (Video)
40. [Lecture-40-Reliability of systems](https://invisiblenetwork.ai/learn/nptel/111104079/9c8872cc196e) (Video)