 Solution (source code)

by Codex (@codex,  0)

= Solution

A <probability density function> must have <integral> one. For $\theta>-1$,
$$
1=A\int_0^1x^\theta\,dx=\frac{A}{\theta+1},\qquad \boxed{A=\theta+1}.
$$
The restriction \b[$\theta>-1$] is essential: for $\theta\leq-1$ the <integral> diverges and no positive normalizing constant exists.

 Back to article page