Probability Foundation for Electrical Engineers (USB)

Media Storage Type : 64 GB USB Stick

NPTEL Subject Matter Expert : Dr. Krishna Jagannathan

NPTEL Co-ordinating Institute : IIT Madras

NPTEL Lecture Count : 96

NPTEL Course Size : 36 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

Lecture 1 - Introduction
Lecture 2 - Cardinality
Lecture 3 - Countability
Lecture 4 - Uncountable sets - 1
Lecture 5 - Uncountable sets - 2
Lecture 6 - Probability spaces - Introduction
Lecture 7 - Probability spaces - Algebra
Lecture 8 - Probability spaces - σ-algebra
Lecture 9 - Probability spaces - Measurable space
Lecture 10 - Properties of probability measures
Lecture 11 - Continuity of probability measure
Lecture 12 - Discrete probability space - finite and countably infinite sample space
Lecture 13 - Discrete probability space - Uncountable sample space
Lecture 14 - Generated σ-algebra, Borel Sets
Lecture 15 - Borel sets
Lecture 16 - Uniform probability measure on Borel sets-Lebesgue measure
Lecture 17 - Carathéodory’s extension theorem
Lecture 18 - Lebesgue measure (Continued...)
Lecture 19 - Infinite coin toss model
Lecture 20 - Infinite coin toss model (Continued...)
Lecture 21 - Conditional probability
Lecture 22 - Properties of conditional probability
Lecture 23 - Independence of events
Lecture 24 - Independence of σ-algebras
Lecture 25 - Borel-Cantelli Lemma - 1
Lecture 26 - Borel-Cantelli Lemma - 2
Lecture 27 - Random Variables
Lecture 28 - Random Variables (Continued...)
Lecture 29 - Cumulative Distribution Function
Lecture 30 - Properties of CDF
Lecture 31 - Types of Random Variables
Lecture 32 - Examples of Random Variables
Lecture 33 - Continuous Random Variables - 1
Lecture 34 - Examples of Continuous Random Variables - 1
Lecture 35 - Continuous Random Variables - 2, Examples of Continuous RandomVariables - 2
Lecture 36 - Singular Random Variables
Lecture 37 - Several Random Variables - 1
Lecture 38 - Several Random Variables - 2
Lecture 39 - Independent Random Variables - 1
Lecture 40 - Independent Random Variables - 2
Lecture 41 - Conditional PMF, Jointly Continuous Random Variables - 1
Lecture 42 - Jointly Continuous Random Variables - 2
Lecture 43 - Jointly Continuous Random Variables - 3
Lecture 44 - Conditional CDF
Lecture 45 - Transformation of Random Variables - 1
Lecture 46 - Transformation of Random Variables - 2; Independent Random Variables
Lecture 47 - Sums of Discrete Random Variables
Lecture 48 - Sums of Jointly Continuous Random Variables
Lecture 49 - Sums of Random Number of Random Variables
Lecture 50 - General Transformations of Random Variables
Lecture 51 - Jacobian Formula
Lecture 52 - Examples Illustrating the use of Jacobian Formula
Lecture 53 - Introduction Integral and Expectation
Lecture 54 - Definition of the Abstract Integral
Lecture 55 - Simple Functions
Lecture 56 - Computing Expectation using Simple Functions, Properties of Integrals
Lecture 57 - Properties of Integrals (Continued....)
Lecture 58 - Inclusion Exclusion Formula using Indicator RVs and Expectation
Lecture 59 - Monotone Convergence Theorem - 1
Lecture 60 - Monotone Convergence Theorem - 2
Lecture 61 - Expectation of a Discrete Random Variable
Lecture 62 - Examples of Expectation of Discrete Random Variables
Lecture 63 - Expectation of Function of Random Variable
Lecture 64 - Some Examples of Computing Expectation
Lecture 65 - Fatou’s Lemma
Lecture 66 - Dominated Convergence Theorem
Lecture 67 - Variance
Lecture 68 - Covariance
Lecture 69 - Covariance Correlation Coefficient - 1
Lecture 70 - Covariance Correlation Coefficient - 2
Lecture 71 - Conditional Expectation
Lecture 72 - Properties of Conditional Expectation
Lecture 73 - MMSE Estimator
Lecture 74 - Transforms
Lecture 75 - Moment Generating Function - 1
Lecture 76 - Moment Generating Function - 2
Lecture 77 - Characteristic Function - 1
Lecture 78 - Characteristic Function - 2
Lecture 79 - Characteristic Function - 3
Lecture 80 - Characteristic Function - 4
Lecture 81 - Concentration Inequalities - 1
Lecture 82 - Concentration Inequalities - 2
Lecture 83 - Convergence of Random Variables - 1
Lecture 84 - Convergence of Random Variables - 2
Lecture 85 - Convergence of Random Variables - 3
Lecture 86 - Convergence of Random Variables - 4
Lecture 87 - Convergence of Random Variables - 5
Lecture 88 - Convergence of Random Variables - 6
Lecture 89 - Convergence Of Characteristic Functions
Lecture 90 - Limit Theorems
Lecture 91 - The Law of Large Numbers - 1
Lecture 92 - The Law of Large Numbers - 2
Lecture 93 - The Central Limit Theorem - 1
Lecture 94 - The Central Limit Theorem - 2
Lecture 95 - A Brief Overview of Multivariate Gaussians - 1
Lecture 96 - A Brief Overview of Multivariate Gaussians - 2