## Proof for a Post a While Back

In a post a while back, I mentioned that I’d found that:

for sufficiently large *k*, which relates to finding the median of the minimum of a set of *k* independent, identically-distributed random variables. I didn’t have a proof at the time, but I’ve thought of a very simple “proof”:

for large *x*.

It’s by no means rigorous, as things that are “approximately equal” put through certain transformations can result in values that are not even close, but it seems to check out in this case.

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Actually, if you perform a series expansion of the LHS of the equation around x = Infinity you will see that the first term is ln2/k. The second one is (ln2)^2/(2k^2), which for k very large is much smaller than the first term. In principle, you are looking at for k –> Infinity. You could also look at for q –> 0 which is easier to treat. Will reply to your email later…

Helmut said this on December 27, 2009 at 9:16 pm |

Ah yes, of course, the Taylor series for about starts with . Thanks! 🙂

Neil Dickson said this on December 28, 2009 at 4:04 am |