Probability Foundations For Electrical Engineers

Course Duration: 12 weeks

PROF. KRISHNA JAGANNATHAN

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What you will learn

  • probability theory

  • signal processing and networking applications

This course will introduce the basic foundational aspects of probability theory primarily to an electrical engineering audience. In communications, signal processing and networking applications, probability theory and models play a vital role in design and implementation. This course will prepare a student to take courses such as Digital/Wireless Communications, Adaptive Signal Processing and Communication Networks.

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Probability spaces-Measurable space
Preview 31:47
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Properties of probability measures
Preview 17:57
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Continuity of probability measure
Preview 31:41
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Discrete probability space-finite and countably infinite sample space
Preview 26:58
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Discrete probability space-Uncountable sample space
Preview 18:11
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Generated σ-algebra, Borel Sets
Preview 26:58
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Borel sets
Preview 25:55
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Uniform probability measure on Borel sets-Lebesgue measure
Preview 24:08

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Carathéodory's extension theorem
Preview 23:53
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Lebesgue measure (contd)
Preview 26:24
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Infinite coin toss model
Preview 25:27
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Infinite coin toss model (Contd)
Preview 23:10
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Conditional probability
Preview 16:56
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Properties of conditional probability
Preview 33:02
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Independence of events
Preview 17:04
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Independence of σ-algebras
Preview 23:32

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Borel-Cantelli Lemma 1
Preview 20:14
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Borel-Cantelli Lemma 2
Preview 30:30
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Random Variables
Preview 22:33
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Random Variables (Contd)
Preview 24:56
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Cumulative Distribution Function
Preview 33:00
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Properties of CDF
Preview 23:06
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Types of Random Variables
Preview 27:25
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Examples of Random Variables
Preview 16:51

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Continuous Random Variables - 1
Preview 22:11
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Examples of Continuous Random Variables - 1
Preview 21:22
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Continuous Random Variables - 2,Examples of Continuous RandomVariables - 2
Preview 21:29
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Singular Random Variables
Preview 25:19
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Several Random Variables - 1
Preview 30:16
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Several Random Variables - 2
Preview 19:05
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Independent Random Variables - 1
Preview 21:27
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Independent Random Variables - 2
Preview 23:44

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Conditional PMF, Jointly Continuous Random Variables - 1
Preview 23:03
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Jointly Continous RandomVariables - 2
Preview 23:53
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Jointly Continuous RandomVariables - 3
Preview 22:33
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Conditional CDF
Preview 23:18
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Transformation of RandomVariables - 1
Preview 28:28
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Transformation of RandomVariables - 2; IndependentRandom Variables
Preview 23:35
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Sums of Discrete RandomVariables
Preview 22:01
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Sums of Jointly ContinuousRandom Variables
Preview 24:08

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Sums of Random Number of Random Variables
Preview 26:49
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General Transformations of Random Variables
Preview 17:16
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Jacobian Formula
Preview 23:23
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Examples Illustrating the use of Jacobian Formula
Preview 24:45
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Introduction Integral and Expectation
Preview 24:30
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Definition of the Abstract Integral
Preview 25:30
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Simple Functions
Preview 23:13
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Computing Expectation using Simple Functions, Properties of Integrals
Preview 19:38

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Properties of Integrals (Contd.)
Preview 24:28
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Inclusion Exclusion Formula using Indicator RVs and Expectation
Preview 26:08
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Monotone Convergence Theorem - 1
Preview 20:25
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Monotone Convergence Theorem - 2
Preview 26:36
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Expectation of a Discrete Random Variable
Preview 23:05
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Examples of Expectation of Discrete Random Variables
Preview 24:09
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Expectation of Function of Random Variable
Preview 20:41
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Some Examples of Computing Expectation
Preview 25:11

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Fatou's Lemma
Preview 23:43
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Dominated Convergence Theorem
Preview 18:15
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Variance
Preview 29:48
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Covariance
Preview 18:38
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Covariance Correlation Coefficient - 1
Preview 18:10
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Covariance Correlation Coefficient - 2
Preview 24:24
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Conditional Expectation
Preview 24:55
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Properties of Conditional Expectation
Preview 28:00

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MMSE Estimator
Preview 15:34
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Transforms
Preview 28:07
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Moment Generating Function - 1
Preview 21:13
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Moment Generating Function - 2
Preview 28:36
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Characteristic Function - 1
Preview 19:13
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Characteristic Function - 2
Preview 30:00
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Characteristic Function - 3
Preview 19:41
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Characteristic Function - 4
Preview 23:24

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Concentration Inequalities - 1
Preview 24:48
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Concentration Inequalities - 2
Preview 21:57
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Convergence of Random Variables - 1
Preview 18:50
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Convergence of Random Variables - 2
Preview 24:26
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Convergence of Random Variables - 3
Preview 24:55
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Convergence of Random Variables - 4
Preview 25:18
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Convergence of Random Variables - 5
Preview 22:16
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Convergence of Random Variables - 6
Preview 23:25

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Convergence Of Characteristic Functions
Preview 21:28
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Limit Theorems
Preview 23:40
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The Law of Large Numbers - 1
Preview 17:10
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The Law of Large Numbers - 2
Preview 31:46
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The Central Limit Theorem - 1
Preview 25:10
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The Central Limit Theorem - 2
Preview 17:56
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A Brief Overview of Multivariate Gaussians - 1
Preview 23:35
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A Brief Overview of Multivariate Gaussians - 2
Preview 35:03

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Live Session 24-09-2020
Preview 56:30
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Meet Your Instructor
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Free

  • Course Duration
    39 h 0 m 13 s
  • Course Level
    Intermediate
  • Student Enrolled
    0
  • Language
    English
This Course Includes
  • 39 h 0 m 13 s Video Lectures
  • 0 Quizzes
  • 0 Assignments
  • 0 Downloadable Resources
  • Full Lifetime Access
  • Certificate of Completion