If X1,X2, . . . ,Xn are independent U(0, 1) random variables and Y=min (X1,X2, . . . ,Xn) has PDF given by

fY(x) = {$\displaystyle n(1-x)^{n-1}$, 0<=x<=1}, 0, otherwise

Identify this distribution, and hence state E[Y] and Var(Y).

Im thinkin it looks similar to a binomial distribution? Am i on the right lines?