There are at least three PDFs which one may encounter. These are the

Uniform distribution $$ \begin{equation*} p(x)=\frac{1}{b-a}\Theta(x-a)\Theta(b-x), \end{equation*} $$ yielding probabilities different from zero in the interval \( [a,b] \).

The exponential distribution $$ \begin{equation*} p(x)=\alpha \exp{(-\alpha x)}, \end{equation*} $$ yielding probabilities different from zero in the interval \( [0,\infty) \) and with mean value $$ \begin{equation*} \mu = \int_0^{\infty}xp(x)dx=\int_0^{\infty}x\alpha \exp{(-\alpha x)}dx=\frac{1}{\alpha}, \end{equation*} $$