the expectation. Common generalization, also due to Erds and Rnyi: as.displaystyle operatorname P bigl (T_m nlog n(m-1)nlog log ncnbigr )to e-e-c m-1)!, textas nto infty. How long on average do we have to wait? The mathematical analysis of the problem reveals that the expected number of trials needed grows as (nlog(n)displaystyle Theta (nlog(n).
Therefore, ti has geometric distribution with expectation 1/. See also edit Here and throughout this article, "log" refers to the natural logarithm rather than a logarithm to some other base. ; Shepp, Lawrence (1960 "The double dixie cup problem American Mathematical Monthly, 67 : 5861, doi :.2307/2308930, MR 0120672 Flajolet, Philippe ; Gardy, Danile; Thimonier, Los (1992 "Birthday paradox, coupon collectors, caching algorithms and self-organizing search", Discrete Applied Mathematics, 39 (3 207229, doi. Here m is fixed. In the general case of a nonuniform probability distribution, according to Philippe Flajolet, 3 E(T)int _0infty big (1-prod _i1n(1-e-p_it)big )dt. Dawkins, Brian (1991 "Siobhan's problem: the coupon collector revisited The American Statistician, 45 (1 7682, doi :.2307/2685247, jstor 2685247. Is the EulerMascheroni constant. 8082, isbn X, MR 1329545. E(50) 50(1 1/2 1/3. Now one can use the Markov inequality to bound the desired probability: P(TcnHn)1c.displaystyle operatorname P (Tgeq cnH_n)leq frac.
Coupon collector s problem - Wikipedia
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