The Distribution Function of the Longest Head Run
Dennis Koh
TL;DR
This paper derives a closed-form analytical expression for the distribution of the longest head run in biased coin tosses by analyzing the related Markov chain of current head runs.
Contribution
It provides the first explicit formula for the distribution function of the longest head run in biased coin tosses, solving a longstanding open problem.
Findings
Derived a closed-form expression for the distribution of the longest head run.
Connected the problem to the Markov chain of current head runs for analysis.
Solved a previously open problem in probability theory.
Abstract
In this paper, the open problem of finding a closed analytical expression for the distribution function of the length of the longest pure head run in coin tosses of a possibly biased coin is solved by studying the closely related Markov chain of current head runs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · Advanced Queuing Theory Analysis · Complex Systems and Time Series Analysis