I have been reading about generating random samples using direct methods. I have come across a definition that if, $X_i ~ Unif(0,1)$ and are i.i.d., then: \begin{align} Y = \frac{\sum_{i=1}^m logX_i}{\sum_{j=1}^{m+n} logX_j} \end{align}
will be a Beta distribution B(m,n). Why is it so and how would i be able to prove the same?