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).


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© 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.

* Address correspondence to this author at the Department of Statistics National Chengchi University No. 64, Sec. 2, ZhiNan Rd., Wenshan District Taipei 11605, Taiwan (R.O.C). Tel: 886-2-29387115; Fax: 886-2-29398024; E-mail: hungy@nccu.edu.tw


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.