NOC:Introduction to Probability Theory and Stochastic Processes


Lecture 1 - Random experiment, sample space, axioms of probability, probability space


Lecture 2 - Random experiment, sample space, axioms of probability, probability space (Continued...)


Lecture 3 - Random experiment, sample space, axioms of probability, probability space (Continued...)


Lecture 4 - Conditional probability, independence of events.


Lecture 5 - Multiplication rule, total probability rule, Bayes's theorem.


Lecture 6 - Definition of Random Variable, Cumulative Distribution Function


Lecture 7 - Definition of Random Variable, Cumulative Distribution Function (Continued...)


Lecture 8 - Definition of Random Variable, Cumulative Distribution Function (Continued...)


Lecture 9 - Type of Random Variables, Probability Mass Function, Probability Density Function


Lecture 10 - Type of Random Variables, Probability Mass Function, Probability Density Function (Continued...)


Lecture 11 - Distribution of Function of Random Variables


Lecture 12 - Mean and Variance


Lecture 13 - Mean and Variance (Continued...)


Lecture 14 - Higher Order Moments and Moments Inequalities


Lecture 15 - Higher Order Moments and Moments Inequalities (Continued...)


Lecture 16 - Generating Functions


Lecture 17 - Generating Functions (Continued...)


Lecture 18 - Common Discrete Distributions


Lecture 19 - Common Discrete Distributions (Continued...)


Lecture 20 - Common Continuous Distributions


Lecture 21 - Common Continuous Distributions (Continued...)


Lecture 22 - Applications of Random Variable


Lecture 23 - Applications of Random Variable (Continued...)


Lecture 24 - Random vector and joint distribution


Lecture 25 - Joint probability mass function


Lecture 26 - Joint probability density function


Lecture 27 - Independent random variables


Lecture 28 - Independent random variables (Continued...)


Lecture 29 - Functions of several random variables


Lecture 30 - Functions of several random variables (Continued...)


Lecture 31 - Some important results


Lecture 32 - Order statistics


Lecture 33 - Conditional distributions


Lecture 34 - Random sum


Lecture 35 - Moments and Covariance


Lecture 36 - Variance Covariance matrix


Lecture 37 - Multivariate Normal distribution


Lecture 38 - Probability generating function and Moment generating function


Lecture 39 - Correlation coefficient


Lecture 40 - Conditional Expectation


Lecture 41 - Conditional Expectation (Continued...)


Lecture 42 - Modes of Convergence


Lecture 43 - Mode of Convergence (Continued...)


Lecture 44 - Law of Large Numbers


Lecture 45 - Central Limit Theorem


Lecture 46 - Central Limit Theorem (Continued...)


Lecture 47 - Motivation for Stochastic Processes


Lecture 48 - Definition of a Stochastic Process


Lecture 49 - Classification of Stochastic Processes


Lecture 50 - Examples of Stochastic Process


Lecture 51 - Examples Of Stochastic Process (Continued...)


Lecture 52 - Bernoulli Process


Lecture 53 - Poisson Process


Lecture 54 - Poisson Process (Continued...)


Lecture 55 - Simple Random Walk


Lecture 56 - Time Series and Related Definitions


Lecture 57 - Strict Sense Stationary Process


Lecture 58 - Wide Sense Stationary Process and Examples


Lecture 59 - Examples of Stationary Processes (Continued...)


Lecture 60 - Discrete Time Markov Chain (DTMC)


Lecture 61 - DTMC (Continued...)


Lecture 62 - Examples of DTMC


Lecture 63 - Examples of DTMC (Continued...)


Lecture 64 - Chapman-Kolmogorov equations and N-step transition matrix


Lecture 65 - Examples based on N-step transition matrix


Lecture 66 - Examples (Continued...)


Lecture 67 - Classification of states


Lecture 68 - Classification of states (Continued...)


Lecture 69 - Calculation of N-Step - 9


Lecture 70 - Calculation of N-Step - 10


Lecture 71 - Limiting and Stationary distributions


Lecture 72 - Limiting and Stationary distributions (Continued...)


Lecture 73 - Continuous time Markov chain (CTMC)


Lecture 74 - CTMC (Continued...)


Lecture 75 - State transition diagram and Chapman-Kolmogorov equation


Lecture 76 - Infinitesimal generator and Kolmogorov differential equations


Lecture 77 - Limiting distribution


Lecture 78 - Limiting and Stationary distributions - 1


Lecture 79 - Birth death process


Lecture 80 - Birth death process (Continued...)


Lecture 81 - Poisson process - 1


Lecture 82 - Poisson process (Continued...)


Lecture 83 - Poisson process (Continued...)


Lecture 84 - Non-homogeneous and compound Poisson process


Lecture 85 - Introduction to Queueing Models and Kendall Notation


Lecture 86 - M/M/1 Queueing Model


Lecture 87 - M/M/1 Queueing Model (Continued...)


Lecture 88 - M/M/1 Queueing Model and Burke's Theorem


Lecture 89 - M/M/c Queueing Model


Lecture 90 - M/M/c (Continued...) and M/M/1/N Model


Lecture 91 - Other Markovian Queueing Models


Lecture 92 - Transient Solution of Finite Capacity Markovian Queues