Let $(X_n)_{n\geq1}$ be iid following a uniform distribution on $]0,1[$. What is the distribution of $Z_n=\prod_{i=1}^n X_i$.
What I did is that I took the log of both sides and found myself with something like $\Pr(\sum_{i=1}^{n} \log(X_i)\leq \log(t)$) and can’t develop further. Can anybody please explain it to me?