Abstract
Suppose that both you and your friend toss an unfair coin n times, for which the probability of heads is equal to α. What is 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 phenomenon as the parameters d, r, and α vary. Our main tools are integral representations based on Fourier analysis.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 731-744 |
| Number of pages | 14 |
| Journal | Journal of Applied Probability |
| Volume | 49 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2012 |
Keywords
- Binomial random variable
- Coin tossing
- Competing random variables
- Number of successes
- Phase transition
- Probability of winning
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty