Wikipedia:Reference desk/Archives/Mathematics/2012 June 22

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June 22

Database attrition

I have a large database from which the records are deleted at the rate of 1/10⁵ every seven years. If I pick five records at random, what is the expectation value for the time at which I will have only three records left? How long to go from three to two? SpinningSpark 23:51, 22 June 2012 (UTC)

See our article on exponential decay. Bo Jacoby (talk) 11:53, 23 June 2012 (UTC).

When there are n records, and each decays at a rate of $1/(7\cdot 10^{5})$, together they decay at a rate of $n/(7\cdot 10^{5}\mathrm {yr} )$, thus it will take on average $(7\cdot 10^{5})/n$ years to go to $n-1$. Thus from 5 to 3 is 315,000 years and from 3 to 2 is 350,000 233,333.3. -- Meni Rosenfeld (talk) 16:58, 24 June 2012 (UTC)

Thanks Meni, that's very helpful. SpinningSpark 23:54, 24 June 2012 (UTC)

Actually, shouldn't 3 to 2 (7/3) be 233,333 years? SpinningSpark 00:01, 25 June 2012 (UTC)

Right, fixed. -- Meni Rosenfeld (talk) 09:27, 27 June 2012 (UTC)