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# About: Discrete Random Variables: Mean or Expected Value and Standard Deviation

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

 Name: Discrete Random Variables: Mean or Expected Value and Standard Deviation ID: m16828 Language: English (en) Summary: This module explores the Law of Large Numbers, the phenomenon where an experiment performed many times will yield cumulative results closer and closer to the theoretical mean over time. Subject: Mathematics and Statistics Keywords: average, discrete, elementary, expected, large, law, long-term, mean, numbers, probability, random, statistics, variable License: Creative Commons Attribution License CC-BY 3.0 Authors: Copyright Holders: Maintainers: Latest version: 1.16 (history) First publication date: May 16, 2008 3:48 pm -0500 Last revision to module: May 27, 2012 12:06 pm -0500

 PDF: m16828_1.16.pdf PDF file, for viewing content offline and printing. Learn more. XML: m16828_1.16.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: 1.16 May 27, 2012 12:06 pm -0500 by Changes: `Discrete Random Variables: Mean or Expected Value and Standard Deviation: Updated notation.` Version: 1.15 May 22, 2012 8:36 am -0500 by Changes: `Discrete Random Variables: Mean or Expected Value and Standard Deviation: Minor word changes.` Version: 1.14 Mar 14, 2012 10:26 am -0500 by Changes: `Module: Discrete Random Variables: Mean or Expected Value and Standard Deviation:Added " A computer randomly selects five numbers from 0 to 9 with replacement" to the example about a game of chance.` Version: 1.13 Aug 11, 2011 10:26 pm -0500 by Changes: `Discrete Random Variables: Mean or Expected Value and Standard Deviation: Updated glossary item "Mean."` Version: 1.12 Feb 23, 2009 4:26 pm -0600 by Changes: `Changed U+02C9 macrons into U+00AF macrons.` Version: 1.11 Feb 6, 2009 7:50 am -0600 by Changes: `Discrete Random Variables: Mean or Expected Value and Standard Deviation: Clarified how to calculate the standard deviation for a discrete probability distribution by cleaning up the language and by showing the calculation. ` Version: 1.10 Jan 25, 2009 6:16 pm -0600 by Changes: `Discrete Random Variables: Mean or Expected Value and Standard Deviation: Corrected some punctuation and changed P(x) to P(X=x) in the glossary.` Version: 1.9 Jan 21, 2009 6:32 pm -0600 by Changes: `Discrete Random Variables: Mean or Expected Value and Standard Deviation: For the last sentence in the first paragraph, ended the sentence after the word "average" for clarity.` Version: 1.8 Jan 21, 2009 3:07 pm -0600 by Changes: `Discrete Random Variables: Mean or Expected Value and Standard Deviation: In the glossary, changed P(x) = P(X=x) since P(x) is the notation for probability function. Also, changed X with a bar over it to lower case x with a bar over it.` Version: 1.7 Oct 27, 2008 2:09 pm -0500 by Changes: `roles updated` Version: 1.6 Jul 16, 2008 2:06 pm -0500 by Changes: `fixed math error and metadata` Version: 1.5 Jul 9, 2008 4:08 am -0500 by Changes: `Post review edits` Version: 1.4 Jul 8, 2008 5:55 pm -0500 by Changes: `post review edits` Version: 1.3 Jul 7, 2008 12:32 pm -0500 by Changes: `post review updates` Version: 1.2 Jun 27, 2008 11:27 am -0500 by Changes: `Roles changed` Version: 1.1 Jun 23, 2008 12:53 am -0500 by Changes: `Initial publication`

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## How to Cite and Attribute This Content

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### American Chemical Society (ACS) Style Guide:

Dean, S.; Illowsky, B. Discrete Random Variables: Mean or Expected Value and Standard Deviation, OpenStax-CNX Web site. http://cnx.org/content/m16828/1.16/, May 27, 2012.

### American Medical Assocation (AMA) Manual of Style:

Dean S, Illowsky B. Discrete Random Variables: Mean or Expected Value and Standard Deviation [OpenStax-CNX Web site]. May 27, 2012. Available at: http://cnx.org/content/m16828/1.16/.

### American Psychological Assocation (APA) Publication Manual:

Dean, S., & Illowsky, B. (2012, May 27). Discrete Random Variables: Mean or Expected Value and Standard Deviation. Retrieved from the OpenStax-CNX Web site: http://cnx.org/content/m16828/1.16/

### Chicago Manual of Style (Bibliography):

Dean, Susan, and Barbara Illowsky. "Discrete Random Variables: Mean or Expected Value and Standard Deviation." OpenStax-CNX. May 27, 2012. http://cnx.org/content/m16828/1.16/.

### Chicago Manual of Style (Note):

Susan Dean and Barbara Illowsky, "Discrete Random Variables: Mean or Expected Value and Standard Deviation," OpenStax-CNX, May 27, 2012, http://cnx.org/content/m16828/1.16/.

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

Dean, S., & Illowsky, B. 2012. Discrete Random Variables: Mean or Expected Value and Standard Deviation. OpenStax-CNX, May 27, 2012. http://cnx.org/content/m16828/1.16/.

### Modern Languages Association (MLA) Style Manual:

Dean, Susan, and Barbara Illowsky. Discrete Random Variables: Mean or Expected Value and Standard Deviation. OpenStax-CNX. 27 May 2012 <http://cnx.org/content/m16828/1.16/>.