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Graph of number of coupons, n vs the expected number of trials (i.e., time) needed to collect them all, E (T ) In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests.
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 ...
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%
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 ...
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 vertices is bounded away from zero. In sufficiently dense graphs distributed according to the Erdős–Rényi model, a giant component exists with high ...
The answer is 11+5/12, assuming the underlying distribution of movie stars per pack is uniform. This is a result of the geometric distribution, = 5/5 + 5/4 + 5/3 + 5/2 + 5/1. = 5( 1/5 + 1/4 + 1/3 + 1/2 + 1/1 ) = 11+5/12. and is related to urn problems, the poisson distribution and generating functions. I have been looking for a proof that the ...
The exploration of the content of a data set. The use to find structure in data. Checking assumptions in statistical models. Communicate the results of an analysis. If one is not using statistical graphics, then one is forfeiting insight into one or more aspects of the underlying structure of the data.
The standard Gumbel distribution is the case where = and = with cumulative distribution function = ()and probability density function = (+).In this case the mode is 0, the median is ( ()), the mean is (the Euler–Mascheroni constant), and the standard deviation is /