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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 standard Collatz function is given by P = 2, a 0 = 1 / 2 , b 0 = 0, a 1 = 3, b 1 = 1. Conway proved that the problem Given g and n, does the sequence of iterates g k (n) reach 1? is undecidable, by representing the halting problem in this way. Closer to the Collatz problem is the following universally quantified problem:
Applications of the harmonic series and its partial sums include Euler's proof that there are infinitely many prime numbers, the analysis of the coupon collector's problem on how many random trials are needed to provide a complete range of responses, the connected components of random graphs, the block-stacking problem on how far over the edge ...
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.
1.1 Coupon collector problem with drawing the coupons in batches of k coupons (with possible repetition in the batch) 2 comments 1.2 Identifying important relationships with too many variables and not enough data
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.
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 ...
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.