A RANDOM WALK APPROACH FOR DERIVING EXACT EXPRESSIONS FOR PROBABILITIES ASSOCIATED WITH EFRON'S BIASED COIN DESIGN

摘要

Markaryan and Rosenberger (2010) derived exact expressions for probabilities associated with Efron's biased coin design by induction, using subtle but somewhat lengthy combinatorial arguments. Concise derivations of these expressions are presented here and are rooted in the geometry of one-dimensional random walks.