Connexions

Sections
You are here: Home » Content » Transform Methods

About: Transform Methods

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

View the content: Transform Methods

Metadata

Name: Transform Methods
ID: m23473
Language: English (en)
Summary: The mathematical expectation E[X] of a random variable locates the center of mass for the induced distribution, and the expectation of the square of the distance between X and E[X] measures the spread of the distribution about its center of mass. These quantities are also known, respectively, as the mean (moment) of X and the variance or second moment of X about the mean. Other moments give added information. We examine the expectation of certain functions of X. Each of these functions involves a parameter, in a manner that completely determines the distribution. We refer to these as transforms. In particular, we consider three of the most useful of these: the moment generating function, the characteristic function, and the generating function for nonnegative, integer-valued random variables.
Subject: Mathematics and Statistics
Keywords: Center of mass, Characteristic function, Generating function, Independence, Integral transforms, Laplace transform, Moment generating function, Moments, Operational properties, Simple random variables, Spread of the distribution, Transforms, Uncorrelated
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: 1.8 (history)
First publication date: Apr 17, 2009 1:01 pm -0500
Last revision to module: Sep 18, 2009 2:01 pm -0500

Downloads

PDF: m23473_1.8.pdf PDF file, for viewing content offline and printing. Learn more.
EPUB: m23473_1.8.epub Electronic publication file, for viewing in handheld devices. Learn more.
XML: m23473_1.8.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.
Source Export ZIP: m23473_1.8.zip ZIP containing the module XML plus any included media files. Can be reimported in the editing interface. Learn more.
Offline ZIP: m23473_1.8_offline.zip An offline HTML copy of the content. Also includes XML, included media files, and other support files. Learn more.

Version History

Version: 1.8 Sep 18, 2009 2:01 pm -0500 by Daniel Williamson
Changes: 
added google analytics tracking code
Version: 1.7 Jul 28, 2009 1:34 pm -0500 by Paul E Pfeiffer
Changes: 
Added summary
Version: 1.6 Jul 28, 2009 1:29 pm -0500 by Paul E Pfeiffer
Changes: 
Added summary
Version: 1.5 Jul 27, 2009 12:18 pm -0500 by Daniel Williamson
Changes: 
disjoint union fix
Version: 1.4 Jun 19, 2009 11:30 am -0500 by Daniel Williamson
Changes: 
m-file fixes, supplemental links, metadata updated
Version: 1.3 Jun 9, 2009 5:30 pm -0500 by Daniel Williamson
Changes: 
updated links, images and accessibility
Version: 1.2 May 26, 2009 4:47 pm -0500 by Daniel Williamson
Changes: 
fixed module names, and updated content structure
Version: 1.1 May 19, 2009 11:24 am -0500 by Paul E Pfeiffer
Changes: 
Cntent

How to Reuse and Attribute This Content

If you derive a copy of this content using a Connexions 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: Transform Methods
  • the Connexions URL where the work can be found: http://cnx.org/content/m23473/1.8/

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. Transform Methods, Connexions Web site. http://cnx.org/content/m23473/1.8/, Sep 18, 2009.

American Medical Assocation (AMA) Manual of Style:

Pfeiffer P. Transform Methods [Connexions Web site]. September 18, 2009. Available at: http://cnx.org/content/m23473/1.8/.

American Psychological Assocation (APA) Publication Manual:

Pfeiffer, P. (2009, September 18). Transform Methods. Retrieved from the Connexions Web site: http://cnx.org/content/m23473/1.8/

Chicago Manual of Style (Bibliography):

Pfeiffer, Paul. "Transform Methods." Connexions. September 18, 2009. http://cnx.org/content/m23473/1.8/.

Chicago Manual of Style (Note):

Paul Pfeiffer, "Transform Methods," Connexions, September 18, 2009, http://cnx.org/content/m23473/1.8/.

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

Pfeiffer, P. 2009. Transform Methods. Connexions, September 18, 2009. http://cnx.org/content/m23473/1.8/.

Modern Languages Association (MLA) Style Manual:

Pfeiffer, Paul. Transform Methods. Connexions. 18 Sep. 2009 <http://cnx.org/content/m23473/1.8/>.