Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Random coin tossing
Download PDF
Download PDF
  • Published: September 1997

Random coin tossing

  • Matthew Harris1 &
  • Michael Keane1 

Probability Theory and Related Fields volume 109, pages 27–37 (1997)Cite this article

  • 161 Accesses

  • 12 Citations

  • Metrics details

Summary.

A sequence of heads and tails is produced by repeatedly selecting a coin from two possible coins, and tossing it. The second coin is tossed at renewal times in a renewal process, and the first coin is tossed at all other times. The first coin is fair (Prob(heads)=1/2), and the second coin is known either to be fair, or to have known biasθ∈(0,1] (Prob(heads) ). Letting u k := Prob (There is a renewal at time k), we show that if ∑ k =0 ∞ u k 2=∞, we can determine, using only the sequence of heads and tails produced, if the second coin had bias θ or 0. If , we show that this is not possible.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, Department of Statistics, Probability and Operations Research, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands e-mail: m.d.harris@twi.tudelft.nl; keane@cwi.nl, , , , , , NL

    Matthew Harris & Michael Keane

Authors
  1. Matthew Harris
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Keane
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 20 November 1996 / In revised form: 20 February 1997

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Harris, M., Keane, M. Random coin tossing. Probab Theory Relat Fields 109, 27–37 (1997). https://doi.org/10.1007/s004400050123

Download citation

  • Issue Date: September 1997

  • DOI: https://doi.org/10.1007/s004400050123

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Mathematics Subject Classification (1991): 60K35
  • 60G30
  • 60G42
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature