Consider the order statistic X(n)=max(X1,…,Xn)X_{(n)} = \max(X_1, \dots, X_n)X(n)=max(X1,…,Xn) for Xi∼Uniform(0,1)X_i \sim \text{Uniform}(0, 1)Xi∼Uniform(0,1). What is the PDF of X(n)X_{(n)}X(n)?
nxn−1n x^{n-1}nxn−1
nxnxnx
xn−1x^{n-1}xn−1
n(1−x)n−1n(1-x)^{n-1}n(1−x)n−1