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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 ...
To do this, we consider the variance of the geometric distribution given in (2) and apply it to the case where n coupons are to be collected. The variance in the sum of the time taken is the sum of the variances of the individual times. This yields: variance σ2 root) can easily be found. The values of μ. is shown.
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 ...
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).
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 ...
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.
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%
Doctors explain if drinking water lowers blood pressure, and the role dehydration plays in high blood pressure. Plus, ways to lower BP naturally.