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