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

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Name: Random Selection
ID: m23652
Language: English (en)
Summary: The usual treatments deal with a single random variable or a fixed, finite number of random variables, considered jointly. However, there are many common applications in which we select at random a member of a class of random variables and observe its value, or select a random number of random variables and obtain some function of those selected. This is formulated with the aid of a counting or selecting random variable N, which is nonegative, integer valued. It may be independent of the class selected, or may be related in some sequential way to members of the class. We consider only the independent case. Many important problems require optional random variables, sometimes called Markov times. These involve more theory than we develop in this treatment. As a basic model, we consider the sum of a random number of members of an iid class. In order to have a concrete interpretation to help visualize the formal patterns, we think of the demand of a random number of customers. We suppose the number of customers N is independent of the individual demands. We formulate a model to be used for a variety of applications. Under standard independence conditions, we obtain expressions for compound demand D, conditional expectation for g(D) given N = n, and moment generating function for D. These are applied in various situations.
Subject: Mathematics and Statistics
Keywords: Basic sequence, Compound demand, Counting random variable, Counting random variables, Incremental sequence, Matlab and compound demand, Random sums
License: Creative Commons Attribution License CC-BY 3.0

Authors: Paul E Pfeiffer (
Copyright Holders: Paul E Pfeiffer (
Maintainers: Paul E Pfeiffer (, Daniel Williamson (, C. Sidney Burrus (

Latest version: 1.6 (history)
First publication date: Apr 17, 2009 5:24 pm -0500
Last revision to module: Sep 18, 2009 1:46 pm -0500


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Version History

Version: 1.6 Sep 18, 2009 1:46 pm -0500 by Daniel Williamson
added google analytics tracking code

Version: 1.5 Jul 27, 2009 12:11 pm -0500 by Daniel Williamson
disjoint union fix

Version: 1.4 Jun 19, 2009 11:23 am -0500 by Daniel Williamson
m-file fixes, supplemental links, metadata updated

Version: 1.3 Jun 9, 2009 5:20 pm -0500 by Daniel Williamson
updated links, images and accessibility

Version: 1.2 May 26, 2009 4:44 pm -0500 by Daniel Williamson
fixed module names, and updated content structure

Version: 1.1 May 20, 2009 1:00 pm -0500 by Paul E Pfeiffer

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