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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 ...
Closer to the Collatz problem is the following universally quantified problem: Given g , does the sequence of iterates g k ( n ) reach 1 , for all n > 0 ? Modifying the condition in this way can make a problem either harder or easier to solve (intuitively, it is harder to justify a positive answer but might be easier to justify a negative one).
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 ...
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 ...
The package-merge algorithm is an O (nL) -time algorithm for finding an optimal length-limited Huffman code for a given distribution on a given alphabet of size n, where no code word is longer than L. It is a greedy algorithm, and a generalization of Huffman's original algorithm. Package-merge works by reducing the code construction problem to ...
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it seems wrong at first ...
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 ...
Python contractors like Rahill and Aycock pick up the cold-blooded creatures year-round, but the challenge provides a chance for their community to “get together” and “share stories” and ...