Say we have a finite population of $N$ points $\{x_1,\dots,x_N\}$, and we draw samples at random without replacement until their sum exceeds some threshold $t$.
We may assume that: $\forall i\ $ $0<x_i<1$, $\sum_{i=1}^{N} x_i=k$ for a known $k$, and that $0<t<k$ is known.
What is the expected number of draws?
Is there a generalization of Wald’s Equation that applies to this case?
Non-trivial bounds would be helpful too.