Roots of Two and the Median of the Minimum
Yet another weird math observation. As k becomes large (like k=1000 has less than 0.034% relative error):
I haven’t actually looked into why this is, but it means that:
So why am I looking at this? Well, I’m really looking at the finding the median of the minimum of k independent, identically-distributed random varaibles. With k such variables:
The question is, what value a is the median of the minimum? Let’s define and solve for it:
If it’s the minimum of many independent variables, it’s then . So, as long as we can find the value a at percentile p of the original distribution, we’ve found the median of this distribution of the minimum. Weird stuff.