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Course11110407940 lectures

Probability Theory and Applications

Prof. Prabha Sharma · IIT Kanpur

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Lectures

Probability Theory and Applications

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

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Prabha Sharma
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
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