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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 ...
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.
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it is a ...
Coupon collector's problem; Ewens sampling formula; References Watterson, G.A. (1975), "On the number of segregating sites in genetical models without ...
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 ...
This phenomenon is closely related to the coupon collector's problem: in order to be connected, a random graph needs enough edges for each vertex to be incident to at least one edge. More precisely, if random edges are added one by one to a graph, then with high probability the first edge whose addition connects the whole graph touches the last ...
Graphs of n vs E(T) in the coupon collector's problem: Image title: Graphs of the number of coupons, n vs the expected number of tries to collect them, E(T) = ceiling(n H(n)) in the coupon collector's problem, drawn by CMG Lee. Width: 100%: Height: 100%
Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma ( γ ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log : Here, ⌊·⌋ represents the floor function .