Learn · Probability Foundations for Electrical Engineers
Lecture 36 of 83week-05
Example: Compute Marginal and Conditional PMFs, Probability of Events
Prof. Andrew Thangaraj and Prof. R. Aravind EE · IIT Madras
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- Probability Foundations for Electrical Engineers, IIT Madras (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Experiments, Outcomes and Events
- Examples: Experiments and sample spaces
- Operations on Events
- Examples: Sample spaces and events
- Sigma Fields and Probability
- Discrete Sample Spaces
- Union and Partition
- Examples: Probability Calculation for Equally likely Outcomes
- Definition and Basic Properties
- Bayes' Rule for Partitions
- Examples: Conditional probability
- Example of Detection
- Example: Coloured Cards from a Box
- Independence of Events
- Examples: Independence
- Combining Independent Experiments
- Conditional Independence
- Examples and Computations with Conditional Independence
- Binomial and Geometric Models
- Examples: Binomial and Geometric Model
- Example: Random walk
- Definition and Discrete Setting
- Random Variables and Events
- Examples: Discrete random variables
- Important distributions
- Examples: Discrete PMFs
- Real-life modeling example
- More Distributions
- Conditional PMFs, Conditioning on an event, Indicator random variables
- Example: Conditioning on an event, Indicator random variables
- Multiple random variables and joint distribution
- Example: Two random variables
- Marginal PMF
- Trinomial joint PMF
- Events and Conditioning with Two Random Variables
- Example: Compute Marginal and Conditional PMFs, Probability of Events
- Independent random variables
- More on independence
- Example: IID Repetitions
- Addition of Random Variables
- Sum, Difference and Max of Two Random Variables
- More Computations: Min of Two Random Variables
- Example: X+Y, X-Y, min(X,Y), max(X,Y)
- Real line as sample space
- Probability density function (pdf)
- Cumulative distribution function (CDF)
- Continuous random variables
- pdf and CDF of Continuous Random Variables
- Spinning pointer example
- Important continuous distributions
- More continuous distributions
- Two-dimensional real sample space
- Joint pdf and joint CDF
- More on assigning probability to regions of x-y plain
- Darts example and marginal pdfs
- Independence to two continuous random variables
- Examples: two independent continuous random variables
- Prob X grater then Y : Computation of Probability of a Non-rectangular Region
- Conditional pdfs for continuous r.v.
- Conditional pdfs (Continued)
- Transformations of random variables
- CDF method
- pdf method
- Examples
- One-to-one transformations
- Expected Value or Mean of a Random Variable
- Properties of Expectation
- Examples: Symmetry
- Expectation Computations for Important Distributions
- Variance
- Examples of Variance
- Correlation and Covariance
- Expectations with two random variables
- Examples: Continuous Distributions
- Examples: Discrete Distributions
- Covariance, continued
- Inequalities or Bounds involving E(.)
- Cauchy-Schwartz Inequality
- Conditional Expectations
- Eg of Conditional Expectations with Uniform r.v (in detail)
- Eg of Conditional Expectations with Poisson r.v (in detail)
- Weak Law of Large Numbers
- Central Limit Theorem (with Examples)