(統計)截切機率分配

 $p.d.f. \ of \ x $ 

$$f(x)=\left\{ \begin{array}{c} 1 &, 0\leq x\leq1\\0 &, otherwise\end{array}\right.$$

求 $f\left(x \vert X\lt \frac{1}{3}\right)$

(1). $f\left(x \vert X\lt \frac{1}{3}\right)=\cfrac{f(x)}{P(X\lt \frac{1}{3} )}=\cfrac{1}{\int_0^{\frac{1}{3}}1dx}=3\quad  , 0\lt x \lt \frac{1}{3}$