Mathematics - Probability Theory and Applications (English)

   Tuesday, April 29, 2025   

Starting a new Lecture Notes Series on Mathematics - Probability Theory and Applications

Youtube Lecture Playlist Credits 

Channel Name: nptelhrd

So Let Us Start to This Journey of Learning 

Mathematics - Probability Theory and Applications By Lecture Notes together!

Lecture 1: Mod-01 Lec-01 Basic principles of counting

Lecture 2: Mod-01 Lec-02 Sample space , events, axioms of probability

Lecture 3: Mod-01 Lec-03 Conditional probability, Independence of events.

Lecture 4: Mod-01 Lec-04 Random variables, cumulative density function, expected value

Lecture 5: Mod-01 Lec-05 Discrete random variables and their distributions

Lecture 6: Mod-01 Lec-06 Discrete random variables and their distributions

Lecture 7: Mod-01 Lec-07 Discrete random variables and their distributions

Lecture 8: Mod-01 Lec-08 Continuous random variables and their distributions.

Lecture 9: Mod-01 Lec-09 Continuous random variables and their distributions.

Lecture 10: Mod-01 Lec-10 Continuous random variables and their distributions.

Lecture 11: Mod-01 Lec-11 Function of random variables, Momement generating function

Lecture 12: Mod-01 Lec-12 Jointly distributed random variables, Independent r. v. and their sums

Lecture 13: Mod-01 Lec-13 Independent r. v. and their sums.

Lecture 14: Mod-01 Lec-14 Chi – square r. v., sums of independent normal r. v., Conditional distr.

Lecture 15: Mod-01 Lec-15 Conditional disti, Joint distr. of functions of r. v., Order statistics

Lecture 16: Mod-01 Lec-16 Order statistics, Covariance and correlation

Lecture 17: Mod-01 Lec-17 Covariance, Correlation, Cauchy- Schwarz inequalities, Conditional expectation.

Lecture 18: Mod-01 Lec-18 Conditional expectation, Best linear predictor

Lecture 19: Mod-01 Lec-19 Inequalities and bounds.

Lecture 20: Mod-01 Lec-20 Convergence and limit theorems

Lecture 21: Mod-01 Lec-21 Central limit theorem

Lecture 22: Mod-01 Lec-22 Applications of central limit theorem

Lecture 23: Mod-01 Lec-23 Strong law of large numbers, Joint mgf.

Lecture 24: Mod-01 Lec-24 Convolutions

Lecture 25: Mod-01 Lec-25 Stochastic processes: Markov process.

Lecture 26: Mod-01 Lec-26 Transition and state probabilities.

Lecture 27: Mod-01 Lec-27 State prob., First passage and First return prob

Lecture 28: Mod-01 Lec-28 First passage and First return prob. Classification of states.

Lecture 29: Mod-01 Lec-29 Random walk, periodic and null states.

Lecture 30: Mod-01 Lec-30 Reducible Markov chains

Lecture 31: Mod-01 Lec-34 Queuing Models: M/M/I, Birth and death process, Little’s formulae

Lecture 32: Mod-01 Lec-35 Analysis of L, Lq ,W and Wq , M/M/S model

Lecture 33: Mod-01 Lec-36 M/M/S , M/M/I/K models

Lecture 34: Mod-01 Lec-31 Time reversible Markov chains

Lecture 35: Mod-01 Lec-37 M/M/I/K and M/M/S/K models

Lecture 36: Mod-01 Lec-38 Application to reliability theory failure law

Lecture 37: Mod-01 Lec-39 Exponential failure law, Weibull law

Lecture 38: Mod-01 Lec-40 Reliability of systems

Lecture 39: Mod-01 Lec-32 Poisson Processes

Lecture 40: Mod-01 Lec-33 Inter-arrival times, Properties of Poisson processes