Previous: 1.9 – Lesson 1 Summary

Next: 2.1 – The Cumulative Distribution Function

Previous: 1.9 – Lesson 1 Summary

Next: 2.1 – The Cumulative Distribution Function

A Set of Open Resources for MATH 105 at UBC

- Home
- About
- Discrete Random Variables
- Continuous Random Variables
- 2.1 – The Cumulative Distribution Function
- 2.2 – A Simple Example
- 2.3 – The Probability Density Function
- 2.4 – A Simple PDF Example
- 2.5 – Some Common Continuous Distributions
- 2.6 – The Normal Distribution
- 2.7 – A Geometric Problem
- 2.8 – Expected Value, Variance, Standard Deviation
- 2.9 – Example
- 2.10 – Lesson 2 Summary

- Additional Problems

Previous: 1.9 – Lesson 1 Summary

Next: 2.1 – The Cumulative Distribution Function

In the previous lesson, we defined random variables in general, but focused only on **discrete** random variables. In this lesson, we properly treat **continuous** random variables.

If for example *X* is the height of a randomly selected person in British Columbia, or *X* is tomorrow's low temperature at Vancouver International Airport, then *X* is a continuously varying quantity.

In this lesson we discuss

- continuous random variables
- the cumulative distribution function
- the probability density function
- expectation, variance and standard deviation of a continuous random variable

Simply reading the content in this lesson will not be sufficient: students will need to complete a sufficient number of Exercises and WeBWorK problems in order to prepare themselves for the final exam.

Previous: 1.9 – Lesson 1 Summary

Next: 2.1 – The Cumulative Distribution Function

### Navigation

- Home
- About
- Discrete Random Variables
- Continuous Random Variables
- 2.1 - The Cumulative Distribution Function
- 2.2 - A Simple Example
- 2.3 - The Probability Density Function
- 2.4 - A Simple PDF Example
- 2.5 - Some Common Continuous Distributions
- 2.6 - The Normal Distribution
- 2.7 - A Geometric Problem
- 2.8 - Expected Value, Variance, Standard Deviation
- 2.9 - Example
- 2.10 - Lesson 2 Summary

- Additional Problems

### Download Lessons

You can download a PDF version of both lessons and additional exercises here.

### Poll

**What is the most difficult concept to understand in probability?***How to calculate a PDF when give a cumulative distribution function. (59%, 303 Votes)*- In MATH 105, there are no difficult topics on probability. (17%, 87 Votes)
- What a random variableĀ is. (14%, 70 Votes)
- The difference between discrete and continuous random variables. (11%, 55 Votes)

Total Voters:

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### Copyright

The content on the MATH 105 Probability Module by The University of British Columbia Mathematics Department has been released into the public domain. Anyone has the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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### Acronyms

Throughout this website, the following acronyms are used.

PDF = probability distribution function

CDF = cumulative distribution function

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