Let $n\in \mathbb N$ and $X_1,\dots,X_{2n}$ independent and uniform distributed on $\{-1,1\},S_i=\sum_{j=1}^i X_j$ Derive the distribution of $X=min\{i:S_i=S_{2n}\}$.
Clearly $S_i$ should be binomial distributed, Then I tried to solve this problem with a combinatorical argument, but could not conclude anything. How should we tackle this problem?