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Activity Number: 507
Type: Contributed
Date/Time: Thursday, August 10, 2006 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Education
Abstract - #306869
Title: A Probability Problem on the Number of Loops Formed When Ends of Strings Are Tied
Author(s): Marepalli Rao*+ and Subramanyam Kasala
Companies: University of Cincinnati and The University of North Carolina at Wilmington
Address: Department of Environmental Health, Cincinnati, OH, 45267,
Keywords: discrete probability ; expected value ; variance ; distribution ; central limit theorem ; senior project
Abstract:

We present a problem from our collection which can be used as a senior project. There are n strings. Each string has two ends. Out of 2n ends, two ends are selected at random and tied. If the two ends come from the same string, we will have a loop right away. If not, we will have (n-1) strings with 2(n-1) ends. We now select two ends at random from these 2(n-1) strings. The process continues until we have one string and its ends are tied. Let X be the total number of loops formed. The possible values of X are 1, 2, ... , n. The project is to calculate the expected value and variance of X and determine the distribution of X.

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