Wald's Identity for the Fair Coin-Tossing Games and Some Applications
Identifiers and Pagination:Year: 2012
First Page: 1
Last Page: 4
Publisher Id: TOSPJ-4-1
Article History:Received Date: 20/12/2011
Revision Received Date: 16/2/2012
Acceptance Date: 19/2/2012
Electronic publication date: 27/7/2012
Collection year: 2012
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.
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.