Probability Foundation for Electrical Engineers

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