Probability Theory and Applications Video Lectures

Probability Theory and Applications
'Probability Theory and Applications' Video Lectures by Prof. Prabha Sharma from IIT Kanpur
"Probability Theory and Applications" - Video Lectures
1. Lecture-01-Basic principles of counting
2. Lecture-02-Sample space , events, axioms of probability
3. Lecture-03-Conditional probability, Independence of events.
4. Lecture-04-Random variables, cumulative density function, expected value
5. Lecture-05-Discrete random variables and their distributions
6. Lecture-06-Discrete random variables and their distributions
7. Lecture-07-Discrete random variables and their distributions
8. Lecture-08-Continuous random variables and their distributions.
9. Lecture-09-Continuous random variables and their distributions.
10. Lecture-10-Continuous random variables and their distributions.
11. Lecture-11-Function of random variables, Momement generating function
12. Lecture-12-Jointly distributed random variables, Independent r. v. and their sums
13. Lecture-13-Independent r. v. and their sums.
14. Lecture-14-Chi – square r. v., sums of independent normal r. v., Conditional distr.
15. Lecture-15 Conditional disti, Joint distr. of functions of r. v., Order statistics
16. Lecture-16-Order statistics, Covariance and correlation.
17. Lecture-17-Covariance, Correlation, Cauchy- Schwarz inequalities, Conditional expectation.
18. Lecture-18-Conditional expectation, Best linear predictor
19. Lecture-19-Inequalities and bounds.
20. Lecture-20-Convergence and limit theorems
21. Lecture-21-Central limit theorem
22. Lecture-22-Applications of central limit theorem
23. Lecture-23-Strong law of large numbers, Joint mgf.
24. Lecture-24-Convolutions
25. Lecture-25-Stochastic processes: Markov process.
26. Lecture-26-Transition and state probabilities.
27. Lecture-27-State prob., First passage and First return prob
28. Lecture-28-First passage and First return prob. Classification of states.
29. Lecture-29-Random walk, periodic and null states.
30. Lecture-30-Reducible Markov chains
31. Lecture-31-Time reversible Markov chains
32. Lecture-32-Poisson Processes
33. Lecture-33-Inter-arrival times, Properties of Poisson processes
34. Lecture-34-Queuing Models: M/M/I, Birth and death process, Little’s formulae
35. Lecture-35-Analysis of L, Lq ,W and Wq , M/M/S model
36. Lecture-36-M/M/S , M/M/I/K models
37. Lecture-37-M/M/I/K and M/M/S/K models
38. Lecture-38-Application to reliability theory failure law
39. Lecture-39-Exponential failure law, Weibull law
40. Lecture-40-Reliability of systems
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