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

= 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?  Spinning Spark  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 $$1/(7\cdot10^5)$$, together they decay at a rate of $$n/(7\cdot10^5\mathrm{yr})$$, thus it will take on average $$(7\cdot10^5)/n$$ 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.  Spinning Spark  23:54, 24 June 2012 (UTC)
 * Actually, shouldn't 3 to 2 (7/3) be 233,333 years?  Spinning Spark  00:01, 25 June 2012 (UTC)
 * Right, fixed. -- Meni Rosenfeld (talk) 09:27, 27 June 2012 (UTC)