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Lecture 4 of 40Probability Theory and Applications

Lecture-04-Random variables, cumulative density function, expected value

Prof. Prabha Sharma · IIT Kanpur

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Probability Theory and Applications, IIT Kanpur (at NPTEL)
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All the lectures

  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