Textbook Problem

In Exercises 79 and 80, (a) show that the nonnegative function is a probability density function, (b) find P(0 ≤ x ≤ 4), and (c) find E(x).

$f(t)=\{\begin{array}{ll}\frac{2}{5}{e}^{-2t/5,}\hfill & t\ge 0\hfill \\ 0,\hfill & t<0\hfill \end{array}$