Let $(X_n)_{n\geq0}$ be a sequence of real $i.i.d$ random variables and $\tau = \inf\{n\geq0 : X_n\in S\}$ with $S \in \mathcal{B}(\mathbb{R}) $
I am trying to find $\tau$'s distribution.
Obviously, $\tau$ is a stopping time in regards to the natural filtration $\sigma(X_0,...,X_n)$ but that's all I could come up with.
Any help would be greatly appreciated.