Let continuous variables $X_1,\ldots,X_k$ be
independently distributed according to the same probability density
function $f(x)$. Prove that the density function for
$\max\{X_1,\ldots,X_k\}$ is given by $kf(x)(F(x))^{k-1}$, where $F$ is
the cumulative distribution for $f$.
Let continuous variables $X_1,\ldots,X_k$ be independently distributed according to the same probability density function $f(x)$. Prove that the density function for $\max\{X_1,\ldots,X_k\}$ is given by $kf(x)(F(x))^{k-1}$, where $F$ is the cumulative distribution for $f$.