# 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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