Distribution of Maximum Order Statistic

• For IID RV $X_1,\dots ,X_n$
• With CDF $F(x)$
• With PDF $f(x)$ Then,
• The distribution of maximum $X_{(n)}$ is $F_{(n)}(x)=[F(x){]}^n$
• The PDF $f_{(n)}(x)=n[F(x){]}^{n-1}f(x)$