Distribution of Minimum Order Statistic

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