Probability: Distribution Models & Continuous Random Variables (edX)

You will learn how these distributions can be connected with the Normal distribution by Central limit theorem (CLT). We will discuss Markov and Chebyshev inequalities, order statistics, moment generating functions and transformation of random variables.

This course along with the recommended pre-requisite, Probability: Basic Concepts & Discrete Random Variables, will you give the skills and knowledge to progress towards an exciting career in information and data science.

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

Syllabus

Units 1 - 6 are available in 416.1x Probability: Basic Concepts & Discrete Random Variables

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