RESEARCH ARTICLE
Wald's Identity for the Fair Coin-Tossing Games and Some Applications
Ying-Chao Hung*
Department of Statistics
National Chengchi University No. 64, Sec. 2, ZhiNan Rd., Wenshan District
Taipei 11605, Taiwan (R.O.C).
Article Information
Identifiers and Pagination:
Year: 2012Volume: 4
First Page: 1
Last Page: 4
Publisher Id: TOSPJ-4-1
DOI: 10.2174/1876527001204010001
Article History:
Received Date: 20/12/2011Revision Received Date: 16/2/2012
Acceptance Date: 19/2/2012
Electronic publication date: 27/7/2012
Collection year: 2012
© 2012 Hung et al.;
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Abstract
We provide a simple proof of Wald's second identity for a class of problems that can be formulated as a fair coin-tossing game. The identity provides a useful technique for computing the expected stopping time and allows us to explore the second-order moment of the so-called heads-minus-tails distribution. We also introduce some interesting applications related to this simple identity.
Keywords: Wald's identity, fair coin-tossing games, heads-minus-tails distribution, stopping time.
