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NPTEL :: Mathematics - NOC:Introduction to Probability Theory and Stochastic Processes
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Course Co-ordinated by :
IIT Delhi
Course Available from :
02-May-2018
NPTEL
Mathematics
NOC:Introduction to Probability Theory and Stochastic Processes (Video)
Random experiment, sample space, axioms of probability, probability space.
Modules / Lectures
Week 1
Random experiment, sample space, axioms of probability, probability space.
Random experiment, sample space, axioms of probability, probability space. (Cont...)
Random experiment, sample space, axioms of probability, probability space. (Contd...)
Conditional probability, independence of events.
Multiplication rule, total probability rule, Bayes's theorem.
Week 2
Definition of Random Variable, Cumulative Distribution Function
Definition of Random Variable, Cumulative Distribution Function (Continued 1)
Definition of Random Variable, Cumulative Distribution Function (Continued 2)
Type of Random Variables, Probability Mass Function, Probability Density Function
Type of Random Variables, Probability Mass Function, Probability Density Function (continued 1)
Distribution of Function of Random Variables
Week 3
Mean and Variance
Mean and Variance Continued
Higher Order Moments and Moments Inequalities
Higher Order Moments and Moments Inequalities Continued
Generating Functions
Generating Functions Continued
Week 4
Common Discrete Distributions
Common Discrete Distributions Continued
Common Continuous Distributions
Common Continuous Distributions Continued
Applications of Random Variable
Applications of Random Variable Continued
Week 5
Random vector and joint distribution
Joint probability mass function
Joint probability density function
Independent random variables
Independent random variables Continued
Week 6
Functions of several random variables
Functions of several random variables continued
Some important results
Order statistics
Conditional distributions
Random sum
Week 7
Moments and Covariance
Variance Covariance matrix
Multivariate Normal distribution
Probability generating function and Moment generating function
Correlation coefficient
Conditional Expectation
Conditional Expectation continued.
Week 8
Modes of Convergence
Mode of Convergence (Continued)
Law of Large Numbers
Central Limit Theorem
Central Limit Theorem (Continued)
Week 9
Motivation for Stochastic Processes
Definition of a Stochastic Process
Classification of Stochastic Processes
Examples of Stochastic Process
Examples Of Stochastic Process (Continued)
Bernoulli Process
Poisson Process
Poisson Process (Continued)
Simple Random Walk
Time Series and Related Definitions
Strict Sense Stationary Process
Wide Sense Stationary Process and Examples
Examples of Stationary Processes Continued
Week 10
Discrete Time Markov Chain (DTMC)
DTMC continued
Examples of DTMC
Examples of DTMC continued
Chapman-Kolmogorov equations and N-step transition matrix
Examples based on N-step transition matrix
Examples continued
Classification of states
Classification of states continued
Calculation of N-Step-9
Calculation of N-Step-10
Limiting and Stationary distributions
Limiting and Stationary distributions continued
Week 11
Continuous time Markov chain (CTMC)
CTMC continued
State transition diagram and Chapman-Kolmogorov equation
Infinitesimal generator and Kolmogorov differential equations
Limiting distribution
Limiting and Stationary distributions -1
Birth death process
Birth death process continued
Poisson process -1
Poisson process continued
Poisson process (cont.)
Non-homogeneous and compound Poisson process
Week 12
Introduction to Queueing Models and Kendall Notation
M/M/1 Queueing Model
M/M/1 Queueing Model Continued...
M/M/1 Queueing Model and Burke's Theorem
M/M/c Queueing Model
M/M/c continued and M/M/1/N Model
Other Markovian Queueing Models
Transient Solution of Finite Capacity Markovian Queues
Translation Feedback form
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