# Story for the cdf $\sim x(1-x)^m$

Let $$U_1,\dots,U_M$$ denote $$M$$ uniform random variables on $$[0,1]$$. The PDF of $$\min_i U_i$$ is proportional to $$(1-x)^{M-1}$$.

Is there such a story for the PDF that is proportional to $$x(1-x)^{M-2}$$?