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Course11110251853 lectures

Introduction to Probability Theory and Stochastic Processes (Tamil)

Prof. S Dharmaraja · IIT Delhi

Start with lecture 1 At NPTEL

About

This course explanations 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 variable, distributions, moments, modes of convergences, classification and properties of stochastic processes, stationary processes, discrete and continuous time Markov chains and simple Markovian queueing models.

Intended audience: UG and research scholars

Prerequisites: Calculus or Mathematics 1

Lectures

Week 1

  1. Lecture 1 : Random Experiment, Sample Space and Sigma Field YouTube
  2. Lecture 2 :Axiomatic Definition of Probability YouTube
  3. Lecture 3 : Properties of Axiomatic Definition of Probability and Classical Definition of Probability YouTube
  4. Lecture 4 : Conditional Probability, Independent Events and Baye's Rule YouTube

Week 2

  1. Lecture 5 : Definition of Random Variable YouTube
  2. Lecture 6 : Cumulative Distribution Function YouTube
  3. Lecture 7 : Discrete and Continuous Type Random Variables YouTube
  4. Lecture 8 : Mixed Type Random Variable YouTube
  5. Lecture 9 : Function of a Random Variable YouTube

Week 3

  1. Lecture 10 : Mean YouTube
  2. Lecture 11 : Variance and higher order moments YouTube
  3. Lecture 12 : Inequalities of Markov and Chebyshev YouTube
  4. Lecture 13 : Generating functions YouTube

Week 4

  1. Lecture 14 : Standard discrete distributions YouTube
  2. Lecture 15 : Standard discrete distributions (continued) YouTube
  3. Lecture 16 : Standard continuous distributions YouTube
  4. Lecture 17 : Standard continuous distributions (continued) YouTube

Week 5

  1. Lecture 18 : Definition and Joint Distribution of a Random Vector YouTube
  2. Lecture 19 : Joint Probability Mass Function YouTube
  3. Lecture 20 : Joint Probability Density Function YouTube
  4. Lecture 21 : Independent Random Vector YouTube

Week 6

  1. Lecture 22 : Distribution of functions of random variables (Discrete type) YouTube
  2. Lecture 23 : Distribution of functions of random variables (Continuous type) YouTube
  3. Lecture 24 : Conditional Distribution of Random Variables (Discrete type) YouTube
  4. Lecture 25 : Conditional Distribution of Random Variables (Continuous type) YouTube

Week 7

  1. Lecture 26 : Expectation for several random variables YouTube
  2. Lecture 27 : Covariance and correlation coefficient YouTube
  3. Lecture 28 : Generating functions for several random variables YouTube
  4. Lecture 29 : Conditional Expectation YouTube

Week 8

  1. Lecture 30 : Modes of convergence YouTube
  2. Lecture 31 : Modes of convergence (contd) YouTube
  3. Lecture 32 : Law of Large Numbers YouTube
  4. Lecture 33 : Central Limit Theorem YouTube

Week 9

  1. Lecture 34 : Definition and Classification of Stochastic Processes YouTube
  2. Lecture 35 : Properties of Stochastic Processes YouTube
  3. Lecture 36 : Properties of Stochastic Processes(Contd) YouTube
  4. Lecture 37 : Standard Simple Stochastic Processes YouTube

Week 10

  1. Lecture 38: Definition of Discrete Time Markov Chain (DTMC) YouTube
  2. Lecture 39: Chapman-Kolmogorov Equation YouTube
  3. Lecture 40: Classification of States YouTube
  4. Lecture 41 : Classification of States (Contd) YouTube
  5. Lecture 42 : Limiting Distribution YouTube
  6. Lecture 43 : Stationary Distribution YouTube
  7. Lecture 44 : Reducible Markov Chains YouTube

Week 11

  1. Lecture 45 : Definition of Continuous Time Markov Chain (CTMC) YouTube
  2. Lecture 46 : Infinitesimal Generator Matrix YouTube
  3. Lecture 47 : Kolmogorov Differential Equations YouTube
  4. Lecture 48 : Limiting Distribution and Steady-State Distribution YouTube
  5. Lecture 49 : Birth Death Processes YouTube

Week 12

  1. Lecture 50 : Introduction to Queueing Models and Kendall Notation YouTube
  2. Lecture 51 : Single-Server Queueing Models YouTube
  3. Lecture 52 : Single-Server Queueing Models (Contd) YouTube
  4. Lecture 53 : Multi-Server Queueing Models YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Delhi
Department
Mathematics
Teacher
Prof. S Dharmaraja
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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