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Coupon collector's problem. In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more ...
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number. The idea of the classification is credited to Gian-Carlo Rota, and the name was ...
Envy-free item allocation. Envy-free (EF) item allocation is a fair item allocation problem, in which the fairness criterion is envy-freeness - each agent should receive a bundle that they believe to be at least as good as the bundle of any other agent. [1] : 296–297.
It is stated that "[The coupon collector's problem] asks the following question: If each box of a brand of cereals contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought to collect all n coupons?" However, this question is not answered in the solution section.
Component (graph theory) In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting of the ...
The expected number of people needed until every birthday is achieved is called the Coupon collector's problem. It can be calculated by nH n , where H n is the n th harmonic number . For 365 possible dates (the birthday problem), the answer is 2365.
Pages in category "Probability problems" The following 31 pages are in this category, out of 31 total. ... Coupon collector's problem; G. Gambler's ruin;
Watterson estimator. In population genetics, the Watterson estimator is a method for describing the genetic diversity in a population. It was developed by Margaret Wu and G. A. Watterson in the 1970s. [ 1][ 2] It is estimated by counting the number of polymorphic sites. It is a measure of the "population mutation rate" (the product of the ...