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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 ...
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.
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 network theory, a giant component is a connected component of a given random graph that contains a significant fraction of the entire graph's vertices . More precisely, in graphs drawn randomly from a probability distribution over arbitrarily large graphs, a giant component is a connected component whose fraction of the overall number of ...
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 ...
Mannequins display the store's new spring fashions at a J.C. Penney store in Queens, New York. (Victor J. Blue/Bloomberg via Getty Images)J.C. Penney's disastrous sales plunge under CEO Ron ...
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.
Merton's portfolio problem. Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice. An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility.