Year: 2010
Type: preprint
Abstract: Suppose you and your friend both do $n$ tosses of an unfair coin with probability of heads equal to $α$. What is the behavior of the probability that you obtain at least $d$ more heads than your friend if you make $r$ additional tosses? We obtain asymptotic and monotonicity/convexity properties for this competing probability as a function of $n$, and demonstrate surprising phase transition phenomenons as parameters $ d, r$ and $α$ vary. Our main tools are integral representations based on Fourier analysis.
Source: arXiv (Cornell University)
Authors: Li, Wenbo V., Vysotsky, Vladislav V.
Institutions: Arizona State University, University of Delaware
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4300054966