Unbiased Coin Tossing with Discrete Random Variables

Abstract

Hoeffding and Simons (Ann. Math. Statist. (1970) 341-352) show how to convert a sequence of i.i.d. indicator random variables with parameter $p$ into such a sequence with parameter $p = \frac{1}{2}$. In the present paper an extension is made to generating sequences of i.i.d. indicator random variables with parameter $p = \frac{1}{2}$ from arbitrary sequences of i.i.d. discrete random variables. Also considered is the generating of sequences of i.i.d. $r$-valued, equiprobable random variables. Some optimality criteria are established.