Random experiment, sample space, axioms of probability, probability space.

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Random experiment, sample space, axioms of probability, probability space. (Cont...)

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Random experiment, sample space, axioms of probability, probability space. (Contd...)

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Conditional probability, independence of events.

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Multiplication rule, total probability rule, Bayes's theorem.

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Definition of Random Variable, Cumulative Distribution Function

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Definition of Random Variable, Cumulative Distribution Function (Continued 1)

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Definition of Random Variable, Cumulative Distribution Function (Continued 2)

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Type of Random Variables, Probability Mass Function, Probability Density Function

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Type of Random Variables, Probability Mass Function, Probability Density Function (continued 1)

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Distribution of Function of Random Variables

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Mean and Variance

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Mean and Variance Continued

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Higher Order Moments and Moments Inequalities

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Higher Order Moments and Moments Inequalities Continued

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Generating Functions

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Generating Functions Continued

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Common Discrete Distributions

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Common Discrete Distributions Continued

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Common Continuous Distributions

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Common Continuous Distributions Continued

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Applications of Random Variable

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Applications of Random Variable Continued

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Random vector and joint distribution

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Joint probability mass function

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Joint probability density function

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Independent random variables

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Independent random variables Continued

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Functions of several random variables

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Functions of several random variables continued

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Some important results

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Order statistics

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Conditional distributions

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Random sum

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Moments and Covariance

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Variance Covariance matrix

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Multivariate Normal distribution

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Probability generating function and Moment generating function

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Correlation coefficient

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Conditional Expectation

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Conditional Expectation continued.

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Modes of Convergence

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Mode of Convergence (Continued)

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Law of Large Numbers

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Central Limit Theorem

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Central Limit Theorem (Continued)

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Motivation for Stochastic Processes

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Definition of a Stochastic Process

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Classification of Stochastic Processes

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Examples of Stochastic Process

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Examples Of Stochastic Process (Continued)

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Bernoulli Process

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Poisson Process

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Poisson Process (Continued)

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Simple Random Walk

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Time Series and Related Definitions

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Strict Sense Stationary Process

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Wide Sense Stationary Process and Examples

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Examples of Stationary Processes Continued

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Discrete Time Markov Chain (DTMC)

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DTMC continued

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Examples of DTMC

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Examples of DTMC continued

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Chapman-Kolmogorov equations and N-step transition matrix

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Examples based on N-step transition matrix

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Examples continued

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Classification of states

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Classification of states continued

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Calculation of N-Step-9

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Calculation of N-Step-10

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Limiting and Stationary distributions

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Limiting and Stationary distributions continued

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Continuous time Markov chain (CTMC)

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CTMC continued

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State transition diagram and Chapman-Kolmogorov equation

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Infinitesimal generator and Kolmogorov differential equations

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Limiting distribution

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Limiting and Stationary distributions -1

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Birth death process

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Birth death process continued

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Poisson process -1

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Poisson process continued

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Poisson process (cont.)

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Non-homogeneous and compound Poisson process

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Introduction to Queueing Models and Kendall Notation

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M/M/1 Queueing Model

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M/M/1 Queueing Model Continued...

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M/M/1 Queueing Model and Burke's Theorem

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M/M/c Queueing Model

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M/M/c continued and M/M/1/N Model

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Other Markovian Queueing Models

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Transient Solution of Finite Capacity Markovian Queues

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