Related papers: Daniel Litt's Probability Puzzle
This paper presents an advance in the direction of working with probabilities in a paracomplete setting using Logics of Formal Undeterminedness (LFUs). The undeterminedness is interpreted here as missing evidence. A theorem of total…
Consider a P\'olya urn with balls of several colours, where balls are drawn sequentially and each drawn ball immediately is replaced together with a fixed number of balls of the same colour. It is well-known that the proportions of balls of…
The article attempts to demonstrate the rich history of one truly remarkable problem situated at the confluence of probability theory and theory of numbers - finding the probability of co-primality of two randomly selected natural numbers.…
This expository paper discusses some conjectures related to visibility and blockers for sets of points in the plane.
We investigate a conjecture of Robert Coleman concerning the module of circular distributions.
In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and…
Uniform probability distributions on $\ell_p$ balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform distribution on the intersection of a…
The problem of assigning probabilities when little is known is analized in the case where the quanities of interest are physical observables, i.e. can be measured and their values expressed by numbers. It is pointed out that the assignment…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
We highlight the different uses of the word 'likelihood' that have arisen in statistics and meteorology, and make the recommendation that one of these uses should be dropped to prevent confusion and misunderstanding.
Sanov's Theorem and the Conditional Limit Theorem (CoLT) are established for a multicolor Polya Eggenberger urn sampling scheme, giving the Polya divergence and the Polya extension to the Maximum Relative Entropy (MaxEnt) method. Polya…
An extended Polya urn Model with two colors, black and white, is studied with some SLLN and CLT on the proportion of white balls.
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which…
We introduce Partiti, the puzzle that will run in Mathematics Magazine in 2018, and use the opportunity to recall some basic properties of integer partitions.
We investigate the complexity of a puzzle that turns out to be NL-complete.
We investigate some natural probability distributions associated with the game of matroid bingo.
The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus hypothetical. In addition, the author expresses his…
This paper develops an analytic theory for the study of some Polya urns with random rules. The idea is to extend the isomorphism theorem in Flajolet et al. (2006), which connects deterministic balanced urns to a differential system for the…
H${\acute{e}}$non [8] used an inclined billiard to investigate aspects of chaotic scattering which occur in satellite encounters and in other situations. His model consisted of a piecewise mapping which described the motion of a point…
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…