*From*: Hubert Chan <hubert@xxxxxxxxx>*To*: hashcash@xxxxxxxxxxxxx*Date*: Thu, 27 May 2004 13:25:34 -0400

>>>>> "Adam" == Adam Back <adam@xxxxxxxxxxxxxxx> writes: [...] Adam> with (discrete) geometric distribution: [...] Adam> I think poisson will approximate to q^n rather than q^n-1, ^^^^^^^ Adam> obviously as b and so n=2^b gets larger (recall p=1/n,q=1-p) they Adam> get asymptotically close. I think you misunderstood me. To approximate a geometric distribution, you use an exponential distribution, not Poisson. Poisson approximates a binomial distribution. (And with the probabilities that we're working with, the approximation should be fairly good.) Poisson gives you the probability of a given number of hits after a fixed time (P_v(n) -- v is supposed to be fixed, not variable, in a Poisson distribution). Exponential gives the probability that the first hit occurs within a given time (P(X<=x) where X is the random variable, and x is the time in question). The analysis seems to be correct. It's just the naming that Anonymous uses is off. http://mathworld.wolfram.com/GeometricDistribution.html http://mathworld.wolfram.com/ExponentialDistribution.html http://mathworld.wolfram.com/BinomialDistribution.html http://mathworld.wolfram.com/PoissonDistribution.html -- Hubert Chan <hubert@xxxxxxxxx> - http://www.uhoreg.ca/ PGP/GnuPG key: 1024D/124B61FA Fingerprint: 96C5 012F 5F74 A5F7 1FF7 5291 AF29 C719 124B 61FA Key available at wwwkeys.pgp.net. Encrypted e-mail preferred.

**References**:**[hashcash] Statistics of hashcash collisions***From:*Anonymous

**[hashcash] geometric vs poisson (Re: Statistics of hashcash collisions)***From:*Adam Back

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