The Open Mathematics, Statistics and Probability Journal

2012, 4 : 1-4
Published online 2012 July 27. DOI: 10.2174/1876527001204010001
Publisher ID: TOSPJ-4-1

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).

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.