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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 46 - Central Limit Theorem (cont.)

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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