The first one is the most basic PDF; namely the uniform distribution $$ \begin{equation} p(x) = \frac{1}{b-a}\theta(x-a)\theta(b-x). \tag{1} \end{equation} $$ For \( a=0 \) and \( b=1 \) we have $$ \begin{array}{ll} p(x)dx = dx & \in [0,1]. \end{array} $$ The latter distribution is used to generate random numbers. For other PDFs, one needs normally a mapping from this distribution to say for example the exponential distribution.