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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 ...
late the probability that two competing collectors will complete the set with the same number of purchases. Other , more complex, variations are provided by Baum and Billingsley (1969) and Sheutzow (2002). References Adler, I., Oren, S. & Ross, S., (2003). The coupon collector’s problem revisited. Journal of Applied Probability, 40(2), 513–518.
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:
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 ...
The consumer does not know which of the coupons in the set they will get until they purchase the product and open the packaging. This situation is sometimes known as the "coupon collector's problem" or "cereal box problem" (since the coupons are often a set of toys found in a packet of cereal).
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.
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.