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