Suppose you have a sum of IID random variables (uniformly distributed in [0, 1])
$$S = \sum_{i=1}^N X_i$$
if I want to have a rough idea of the average value of $N$ such that the sum is equal to some number $S_0$ is it safe to say that $N$ is going to be around $S_0/{\rm E}[X_i]$ (assuming I'm not under the conditions of using Martingale).
UPDATE: I reformulate the problem. Suppose $N$ is a random variable defined as the smallest integer such that $$ \sum_{i=1}^N X_i \geq S_0 $$ where $X_i$ are IID and uniformly distributed in $[0, x_0]$, with $x_0 < S_0$. What is $E[N]$?