OpenStax CNX

Sections
You are here: Home » Content » Distribution and Density Functions

About: Distribution and Density Functions

Module by: Paul E Pfeiffer. E-mail the author

View the content: Distribution and Density Functions

Metadata

Name: Distribution and Density Functions
ID: m23267
Language: English (en)
Summary: In the unit on Random Variables and Probability, we introduce real random variables as mappings from the basic space to the real line. The mapping induces a transfer of the probability mass on the basic space to subsets of the real line in such a way that the probability that X takes a value in a set M is exactly the mass assigned to that set by the transfer. To perform probability calculations, we need to describe analytically the distribution on the line. For simple random variables, we have at each possible value of X a point mass equal to the probability X takes that value. For more general cases, we need a more useful description: the distribution function which at each t has the value of the probability mass at or to the left of t. If the probability mass in the induced distribution is spread smoothly along the real line, with no point mass concentrations, there is a probability density function such that the probability mass in any interval is the area under the curve over that interval.
Subject: Mathematics and Statistics
Keywords: Beta, Binomial, Common discrete distributions, Distribution function, Exponential, Gamma, Geometric, Negative binomial, Normal or Gaussian, Poisson, Simple random variable, Symmetric triangular, Uniform, Weibull
License: Creative Commons Attribution License CC-BY 3.0

Authors: Paul E Pfeiffer (perhp@earthlink.net)
Copyright Holders: Paul E Pfeiffer (perhp@earthlink.net)
Maintainers: Paul E Pfeiffer (perhp@earthlink.net), Daniel Williamson (dcwill@cnx.org), C. Sidney Burrus (csb@rice.edu)

Latest version: 1.7 (history)
First publication date: Apr 15, 2009 3:56 pm -0500
Last revision to module: Sep 18, 2009 12:32 pm -0500

Downloads

PDF: m23267_1.7.pdf PDF file, for viewing content offline and printing. Learn more.
XML: m23267_1.7.cnxml XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more.

Version History

Version: 1.7 Sep 18, 2009 12:32 pm -0500 by Daniel Williamson
Changes:
added google analytics tracking code

Version: 1.6 Jul 27, 2009 11:52 am -0500 by Daniel Williamson
Changes:
disjoint union fix

Version: 1.5 Jun 19, 2009 11:03 am -0500 by Daniel Williamson
Changes:
m-file fixes, supplemental links, metadata updated

Version: 1.4 Jun 9, 2009 5:05 pm -0500 by Daniel Williamson
Changes:
updated links, images, and accessibility

Version: 1.3 May 26, 2009 4:22 pm -0500 by Daniel Williamson
Changes:
fixed module names, and updated content structure

Version: 1.2 May 14, 2009 2:52 pm -0500 by Paul E Pfeiffer
Changes:
content

Version: 1.1 May 13, 2009 5:18 pm -0500 by Paul E Pfeiffer
Changes:
initial

How to Reuse and Attribute This Content

If you derive a copy of this content using a OpenStax_CNX account and publish your version, proper attribution of the original work will be automatically done for you.

If you reuse this work elsewhere, in order to comply with the attribution requirements of the license (CC-BY 3.0), you must include

  • the authors' names: Paul Pfeiffer
  • the title of the work: Distribution and Density Functions
  • the OpenStax_CNX URL where the work can be found: http://cnx.org/content/m23267/1.7/

See the citation section below for examples you can copy.

How to Cite and Attribute This Content

The following citation styles comply with the attribution requirements for the license (CC-BY 3.0) of this work:

American Chemical Society (ACS) Style Guide:

Pfeiffer, P. Distribution and Density Functions, OpenStax_CNX Web site. http://cnx.org/content/m23267/1.7/, Sep 18, 2009.

American Medical Assocation (AMA) Manual of Style:

Pfeiffer P. Distribution and Density Functions [OpenStax_CNX Web site]. September 18, 2009. Available at: http://cnx.org/content/m23267/1.7/.

American Psychological Assocation (APA) Publication Manual:

Pfeiffer, P. (2009, September 18). Distribution and Density Functions. Retrieved from the OpenStax_CNX Web site: http://cnx.org/content/m23267/1.7/

Chicago Manual of Style (Bibliography):

Pfeiffer, Paul. "Distribution and Density Functions." OpenStax_CNX. September 18, 2009. http://cnx.org/content/m23267/1.7/.

Chicago Manual of Style (Note):

Paul Pfeiffer, "Distribution and Density Functions," OpenStax_CNX, September 18, 2009, http://cnx.org/content/m23267/1.7/.

Chicago Manual of Style (Reference, in Author-Date style):

Pfeiffer, P. 2009. Distribution and Density Functions. OpenStax_CNX, September 18, 2009. http://cnx.org/content/m23267/1.7/.

Modern Languages Association (MLA) Style Manual:

Pfeiffer, Paul. Distribution and Density Functions. OpenStax_CNX. 18 Sep. 2009 <http://cnx.org/content/m23267/1.7/>.