Probability: Distribution Models & Continuous Random Variables

Learn about probability distribution models, including normal distribution, and continuous random variables to prepare for a career in information and data science.
This course is archived
Estimated 6 weeks
4–6 hours per week
Self-paced
Free

In this statistics and data analysis course, you will learn about continuous random variables and some of the most frequently used probability distribution models including, exponential distribution, Gamma distribution, Beta distribution, and most importantly, normal distribution.

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.

The Center for Science of Information, a National Science Foundation Center, supports learners by offering free educational resources in information science.

At a glance

• Language: English
• Video Transcript: English

What you'll learn

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• 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

Syllabus

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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

Learner testimonials

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"The content of this course is very appealing, awesome, and very thorough. Thank you very much! – Previous Student