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October 31st, 2015, 08:23 AM   #1
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N random numbers with constant sum

Hi all,

I would like to ask if the problem described below has been solved or if you can give me some guidelines in order to solve it.

Problem:

We have $\displaystyle N$ random numbers in [$\displaystyle 0, 1$]with a constant sum of $\displaystyle 1$ (e.g. 0.2, 0.3 and 0.5). We want to find a subset of these numbers which has a sum as close as possible to $\displaystyle a$, where $\displaystyle 0<=a<=1$. So, $\displaystyle a$ is the ideal sum of the subset and let's denote $\displaystyle b$ the real sum (The sum of a subset which is as close as possible to $\displaystyle a$). So, in our example, if $\displaystyle a=0.65$, then the subset {$\displaystyle 0.5, 0.2$} with a sum of $\displaystyle 0.7$ is the closest one. I would like to calculate the mean difference $\displaystyle |b-a|$ as a function of $\displaystyle a $ and $\displaystyle N$. Any ideas on this? For example, what kind of distribution the $\displaystyle N$ random numbers follow?

Thank you in advance
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