I like to split a given interval, let's say $[0,1]$, randomly to a given number $n$ parts.
A random input may be provided, like for example a sequence of random numbers $\omega=(r1, r2, ...)\in\Omega$, as usual random number generators generate.
Is there any efficiently computable function $F_\omega(i), i\in 0,..,n$ that gives a random partition with $$F_\omega(k)=\sum_{i\in 0..k} f_\omega(i)$$ so that $F_\omega(n)=1$ and $F(0), ..., F(n)$ will distribute in a evenly fashion, eg. $F_\omega(i)$ with randomly choosen $i$ will have a uniform distribution?
Like a cake cut at $n$ randomly choosen angles...