Models of Coin-Tossing for Markov Chains. Revision
Abstract
Models of coin-tossing have been considered both in their own aspect or as specialized Markov chains. A typical model calls for tossing a (biased) coin until a certain well defined stopping event, the target, terminates the tossing; the random variable of interest, the tally, is the number of tosses. This report extended the Feller-type models in several ways, all believed to be new: Target event of variable length, e.g. h-odd number tails -h. It allows tally variables other than number of tosses, e.g. number of heads, number of tails, number of runs, number of doublets ht on way to the stopping event, etc. It allows vector-valued tallies. A central result shows how to mechanically transform an existing solution (usually in the form of a generating function) for the number of tosses into a joint solution for the number of heads and tails. A beginning is made towards expressing the tally process in terms of simpler building blocks, in particular geometric random variables in many instances a tossing model can be solved from the knowledge of several initial probabilities but some more work remains to be done to develop this method, which is essentially the method of indetermined coefficients.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 11, 1987
- Accession Number
- ADA196572
Entities
People
- Martin Krakowski
Organizations
- George Mason University