Related papers: A probabilistic way to discover the rainbow
The Secret Santa ritual, where in a group of people every member presents a gift to a randomly assigned partner, poses a combinatorial problem when considering the probabilities involved in the formation of pairs, where two persons exchange…
There are two methods for counting the number of occurrences of a string in another large string. One is to count the number of places where the string is found. The other is to determine how many pieces of string can be extracted without…
Binomial distributions capture the probabilities of `heads' outcomes when a (biased) coin is tossed multiple times. The coin may be identified with a distribution on the two-element set {0,1}, where the 1 outcome corresponds to `head'. One…
In this paper, we study the problem of splitting fairly bundles of items. We show that given $n$ bundles with $m$ kinds of items in them, it is possible to distribute the value of each kind of item fairly among $r$ persons by breaking apart…
How can we select a cohort of promising astrophysicists before they have made their discoveries? This is the fundamental challenge of academic planning. I argue that science can only blossom if young researchers are rewarded for acquired…
The study of several naturally arising "nearest neighbours" random walks benefits from the study of the associated orthogonal polynomials and their orthogonality measure. I consider extensions of this approach to a larger class of random…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
We give a series of combinatorial results that can be obtained from any two collections (both indexed by $\Z\times \N$) of left and right pointing arrows that satisfy some natural relationship. When applied to certain self-interacting…
Clinicians and scientists have traditionally focussed on whether their findings will be replicated and are very familiar with the concept. The probability that a replication study yields an effect with the same sign, or the same statistical…
In this note, we introduce a distributed twist on the classic coupon collector problem: a set of $m$ collectors wish to each obtain a set of $n$ coupons; for this, they can each sample coupons uniformly at random, but can also meet in…
We propose an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. that two histograms are drawn from the same distribution). The…
Organisms and algorithms learn probability distributions from previous observations, either over evolutionary time or on the fly. In the absence of regularities, estimating the underlying distribution from data would require observing each…
Detecting butterfly hybrids requires knowledge of the parent subspecies, and the process can be tedious when encountering a new subspecies. This study focuses on a specific scenario where a model trained to recognize hybrid species A can…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
The Monty Hall puzzle has been solved and dissected in many ways, but always using probabilistic arguments, so it is considered a probability puzzle. In this paper the puzzle is set up as an orthodox statistical problem involving an unknown…
When people pursue rewards in stochastic environments, they often match their choice frequencies to the observed target frequencies, even when this policy is demonstrably sub-optimal. We used a ``hide and seek'' task to evaluate this…
The work describes a general problem, which emphasizes proportional reasoning and probabilistic reasoning skills in the context of planting garlic in a backyard garden. Along with practicing these reasoning skills in a context far-removed…
Children can take many paths to become scientists. But they undoubtedly include the following steps Play, play and play; Observe; Ask (themselves). In this paper I will talk about some of my experiences teaching girls and boys, teenagers…
Despite being a major component in the teaching of special relativity, the twin `paradox' is generally not examined in courses on general relativity. Due to the complexity of analytical solutions to the problem, the paradox is often…
We consider an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. two histograms are drawn from the same distribution). The…