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Course10810610683 lectures

Probability Foundations for Electrical Engineers

Prof. Andrew Thangaraj and Prof. R. Aravind EE · IIT Madras

Start with lecture 1 At NPTEL

Lectures

week-00

  1. Experiments, Outcomes and Events Video
  2. Examples: Experiments and sample spaces Video

week-01

  1. Operations on Events Video
  2. Examples: Sample spaces and events Video
  3. Sigma Fields and Probability Video
  4. Discrete Sample Spaces Video
  5. Union and Partition Video
  6. Examples: Probability Calculation for Equally likely Outcomes Video

week-02

  1. Definition and Basic Properties Video
  2. Bayes' Rule for Partitions Video
  3. Examples: Conditional probability Video
  4. Example of Detection Video
  5. Example: Coloured Cards from a Box Video

week-03

  1. Independence of Events Video
  2. Examples: Independence Video
  3. Combining Independent Experiments Video
  4. Conditional Independence Video
  5. Examples and Computations with Conditional Independence Video
  6. Binomial and Geometric Models Video
  7. Examples: Binomial and Geometric Model Video
  8. Example: Random walk Video

week-04

  1. Definition and Discrete Setting Video
  2. Random Variables and Events Video
  3. Examples: Discrete random variables Video
  4. Important distributions Video
  5. Examples: Discrete PMFs Video
  6. Real-life modeling example Video
  7. More Distributions Video

week-05

  1. Conditional PMFs, Conditioning on an event, Indicator random variables Video
  2. Example: Conditioning on an event, Indicator random variables Video
  3. Multiple random variables and joint distribution Video
  4. Example: Two random variables Video
  5. Marginal PMF Video
  6. Trinomial joint PMF Video
  7. Events and Conditioning with Two Random Variables Video
  8. Example: Compute Marginal and Conditional PMFs, Probability of Events Video

week-06

  1. Independent random variables Video
  2. More on independence Video
  3. Example: IID Repetitions Video
  4. Addition of Random Variables Video
  5. Sum, Difference and Max of Two Random Variables Video
  6. More Computations: Min of Two Random Variables Video
  7. Example: X+Y, X-Y, min(X,Y), max(X,Y) Video

week-07

  1. Real line as sample space Video
  2. Probability density function (pdf) Video
  3. Cumulative distribution function (CDF) Video
  4. Continuous random variables Video
  5. pdf and CDF of Continuous Random Variables Video
  6. Spinning pointer example Video
  7. Important continuous distributions Video
  8. More continuous distributions Video

week-08

  1. Two-dimensional real sample space Video
  2. Joint pdf and joint CDF Video
  3. More on assigning probability to regions of x-y plain Video
  4. Darts example and marginal pdfs Video
  5. Independence to two continuous random variables Video
  6. Examples: two independent continuous random variables Video
  7. Prob X grater then Y : Computation of Probability of a Non-rectangular Region Video
  8. Conditional pdfs for continuous r.v. Video
  9. Conditional pdfs (Continued) Video

week-09

  1. Transformations of random variables Video
  2. CDF method Video
  3. pdf method Video
  4. Examples Video
  5. One-to-one transformations Video
  6. Expected Value or Mean of a Random Variable Video
  7. Properties of Expectation Video
  8. Examples: Symmetry Video

week-10

  1. Expectation Computations for Important Distributions Video
  2. Variance Video
  3. Examples of Variance Video
  4. Correlation and Covariance Video
  5. Expectations with two random variables Video
  6. Examples: Continuous Distributions Video
  7. Examples: Discrete Distributions Video

week-11

  1. Covariance, continued Video
  2. Inequalities or Bounds involving E(.) Video
  3. Cauchy-Schwartz Inequality Video
  4. Conditional Expectations Video
  5. Eg of Conditional Expectations with Uniform r.v (in detail) Video
  6. Eg of Conditional Expectations with Poisson r.v (in detail) Video

week-12

  1. Weak Law of Large Numbers Video
  2. Central Limit Theorem (with Examples) Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Electrical Engineering
Taught by
Prof. Andrew Thangaraj, Prof. R. Aravind EE
Level
Undergraduate
Language
English
Subjects
Engineering
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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