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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