NOC:Probability Foundations for Electrical Engineers


Lecture 1 - Experiments, Outcomes and Events


Lecture 2 - Examples: Experiments and sample spaces


Lecture 3 - Operations on Events


Lecture 4 - Examples: Sample spaces and events


Lecture 5 - Sigma Fields and Probability


Lecture 6 - Discrete Sample Spaces


Lecture 7 - Union and Partition


Lecture 8 - Examples: Probability Calculation for Equally likely Outcomes


Lecture 9 - Definition and Basic Properties


Lecture 10 - Bayes' Rule for Partitions


Lecture 11 - Examples: Conditional probability


Lecture 12 - Example of Detection


Lecture 13 - Example: Coloured Cards from a Box


Lecture 14 - Independence of Events


Lecture 15 - Examples: Independence


Lecture 16 - Combining Independent Experiments


Lecture 17 - Conditional Independence


Lecture 18 - Examples and Computations with Conditional Independence


Lecture 19 - Binomial and Geometric Models


Lecture 20 - Examples: Binomial and Geometric Model


Lecture 21 - Definition and Discrete Setting


Lecture 22 - RandomVariables and Events


Lecture 23 - Examples: Discrete random variables


Lecture 24 - Important distributions


Lecture 25 - Examples: Discrete PMFs


Lecture 26 - Real-life modeling example


Lecture 27 - More Distributions


Lecture 28 - Conditional PMFs, Conditioning on an event, Indicator random variables


Lecture 29 - Example: Conditioning on an event, Indicator random variables


Lecture 30 - Multiple random variables and joint distribution


Lecture 31 - Example: Two random variables


Lecture 32 - Marginal PMF


Lecture 33 - Trinomial joint PMF


Lecture 34 - Events and Conditioning with Two Random Variables


Lecture 35 - Example: compute marginal and conditional PMFs, probability of events


Lecture 36 - Independent random variables


Lecture 37 - More on independence


Lecture 38 - Example: IID Repetitions


Lecture 39 - Addition of Random Variables


Lecture 40 - Sum, Difference and Max of Two Random Variables


Lecture 41 - More Computations: Min of Two Random Variables


Lecture 42 - Example: X+Y, X-Y, min(X,Y), max(X,Y)


Lecture 43 - Real line as sample space


Lecture 44 - Probability density function (pdf)


Lecture 45 - Cumulative distribution function (CDF)


Lecture 46 - Continuous random variables


Lecture 47 - pdf and CDF of continuous random variables


Lecture 48 - Spinning pointer example


Lecture 49 - Important continuous distributions


Lecture 50 - More continuous distributions


Lecture 51 - Two-dimensional real sample space


Lecture 52 - Joint pdf and joint CDF


Lecture 53 - More on assigning probability to regions of x-y plain


Lecture 54 - Darts example and marginal pdfs


Lecture 55 - Independence to two continuous random variables


Lecture 56 - Examples: two independent continuous random variables


Lecture 57 - Prob[ X > Y ]: computation of probability of a non-rectangular region


Lecture 58 - Transformations of random variables


Lecture 59 - CDF method


Lecture 60 - pdf method


Lecture 61 - Examples


Lecture 62 - One-to-one transformations


Lecture 63 - Expected Value or Mean of a Random Variable


Lecture 64 - Properties of Expectation


Lecture 65 - Expectation Computations for Important Distributions


Lecture 66 - Variance


Lecture 67 - Examples of Variance


Lecture 68 - Expectations with Two Random Variables


Lecture 69 - Correlation and Covariance


Lecture 70 - Examples: Continuous Distributions


Lecture 71 - Examples: Symmetry


Lecture 72 - Examples: Discrete Distributions


Lecture 73 - Live Session