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Probability: Distributions & Continuous Random Variables




Also available on: edX

Overview

 

Learn about probability distribution models, including normal distribution, and continuous random variables to prepare for a career in information and data science.

This is part 2 of 2. Part 1 is available here: https://www.youtube.com/playlist?list=PLNAxrEh0NNf428tm3dhwcbVdviEWpoj6S

Part 2 (Units 7-12) is also available as a free course on edX (certificate available): https://www.edx.org/course/probability-basic-concepts-discrete-random-variables

What you’ll learn:

  • Probability concepts and rules.
  • Some of the most widely used probability models with continuous random variables.
  • How distribution models we have encountered connect with Normal distribution.
  • Advanced probability topics

Description for each Unit: (units 1-6 are available in part 1: https://www.youtube.com/playlist?list=PLNAxrEh0NNf428tm3dhwcbVdviEWpoj6S )

Unit 7: Continuous Random Variables In this unit, we start from the instruction of continuous random variables, then discuss the joint density/CDF and properties of independent continuous random variables.

Unit 8: Conditional Distributions and Expected Values Conditional distributions for continuous random variables, expected values of continuous random variables, and expected values of functions of random variables.

Unit 9: Models of Continuous Random Variables In this unit we will discuss four common distribution models of continuous random variables: Uniform, Exponential, Gamma and Beta distributions.

Unit 10: Normal Distribution and Central Limit Theorem (CLT) Introduction to Normal distribution and CLT, as well as examples of how CLT can be used to approximate models of continuous uniform, Gamma, Binomial, Bernoulli and Poisson.

Unit 11: Covariance, Conditional Expectation, Markov and Chebychev Inequalities Unit

12: Order Statistics, Moment Generating Functions, Transformation of RVs

Instructors and motivated learners: view all of the resources (lessons, examples, problems sets, etc) associated with this video: http://llc.stat.purdue.edu/2017/41600/

 

Module Author

Syllabus/Suggested Schedule

To view any lecture, just click on them and view it in the player above

 


Unit 7: Continuous Random Variables

 

In this unit, we start from the instruction of continuous random variables, then discuss the joint density/CDF and properties of independent continuous random variables.

 

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Unit 8: Conditional Distributions and Expected Values

 

Conditional distributions for continuous random variables, expected values of continuous random variables, and expected values of functions of random variables.

 

  • Unit 8: prob2701
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Unit 9: Models of Continuous Random Variables

 

In this unit we will discuss four common distribution models of continuous random variables: Uniform, Exponential, Gamma and Beta distributions.

 

  • Unit 9: prob3101
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Unit 10: Normal Distribution and Central Limit Theorem (CLT)

 

Introduction to Normal distribution and CLT, as well as examples of how CLT can be used to approximate models of continuous uniform, Gamma, Binomial, Bernoulli and Poisson.

 

  • Unit 10: prob3501
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Unit 11: Covariance, Conditional Expectation, Markov and Chebychev Inequalities

  • Unit 11: prob3901
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Unit 12: Order Statistics, Moment Generating Functions, Transformation of RVs

  • Unit 12: prob4201
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