Introduction to Probability Theory and Stochastic Processes
Introduction to Probability Theory and Stochastic Processes. Instructor: Prof. S. Dharmaraja, Department of Mathematics, IIT Delhi. This course is an explanation and expositions of probability and stochastic processes concepts which they need for their experiments and research. It also covers theoretical concepts of probability and stochastic processes pertaining to handling various stochastic modeling. This course provides random variables, distributions, moments, modes of convergence, classification and properties of stochastic processes, stationary processes, discrete and continuous time Markov chains and simple Markovian queueing models.
(from nptel.ac.in)
| Lecture 01 - Random Experiment, Sample Space, Axioms of Probability, Probability Space |
| Lecture 02 - Random Experiment, Sample Space, Axioms of Probability, Probability Space (cont.) |
| Lecture 03 - Random Experiment, Sample Space, Axioms of Probability, Probability Space (cont.) |
| Lecture 04 - Conditional Probability, Independence of Events |
| Lecture 05 - Multiplication Rule, Total Probability Rule, Bayes Theorem |
| Lecture 06 - Definition of Random Variable, Cumulative Distribution Function |
| Lecture 07 - Definition of Random Variable, Cumulative Distribution Function (cont.) |
| Lecture 08 - Definition of Random Variable, Cumulative Distribution Function (cont.) |
| Lecture 09 - Type of Random Variables, Probability Mass Function, Probability Density Function |
| Lecture 10 - Type of Random Variables, Probability Mass Function, Probability Density Function (cont.) |
| Lecture 11 - Distribution of Function of Random Variables |
| Lecture 12 - Mean and Variance |
| Lecture 13 - Mean and Variance (cont.) |
| Lecture 14 - Higher Order Moments and Moments Inequalities |
| Lecture 15 - Higher Order Moments and Moments Inequalities (cont.) |
| Lecture 16 - Generating Functions |
| Lecture 17 - Generating Functions (cont.) |
| Lecture 18 - Common Discrete Distributions |
| Lecture 19 - Common Discrete Distributions (cont.) |
| Lecture 20 - Common Continuous Distributions |
| Lecture 21 - Common Continuous Distributions (cont.) |
| Lecture 22 - Applications of Random Variable |
| Lecture 23 - Applications of Random Variable (cont.) |
| 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 (cont.) |
| Lecture 29 - Functions of Several Random Variables |
| Lecture 30 - Functions of Several Random Variables (cont.) |
| 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 (cont.) |
| Lecture 42 - Modes of Convergence |
| Lecture 43 - Modes of Convergence (cont.) |
| Lecture 44 - Law of Large Numbers |
| Lecture 45 - Central Limit Theorem |
| Lecture 46 - Central Limit Theorem (cont.) |
| 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 (cont.) |
| Lecture 52 - Bernoulli Process |
| Lecture 53 - Poisson Process |
| Lecture 54 - Poisson Process (cont.) |
| 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 (cont.) |
| Lecture 60 - Discrete Time Markov Chain (DTMC) |
| Lecture 61 - DTMC (cont.) |
| Lecture 62 - Examples of DTMC |
| Lecture 63 - Examples of DTMC (cont.) |
| Lecture 64 - Chapman-Kolmogorov Equations and N-Step Transition Matrix |
| Lecture 65 - Examples Based on N-Step Transition Matrix |
| Lecture 66 - Examples Based on N-Step Transition Matrix (cont.) |
| Lecture 67 - Classification of States |
| Lecture 68 - Classification of States (cont.) |
| 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 (cont.) |
| Lecture 73 - Continuous Time Markov Chain (CTMC) |
| Lecture 74 - CTMC (cont.) |
| 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 |
| Lecture 79 - Birth Death Process |
| Lecture 80 - Birth Death Process (cont.) |
| Lecture 81 - Poisson Process |
| Lecture 82 - Poisson Process (cont.) |
| Lecture 83 - Poisson Process (cont.) |
| Lecture 84 - Nonhomogeneous 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 (cont.) |
| 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 Capability Markovian Queues |