Chapter 8.8, Problem 80E

(a)

To determine

To prove: That the non-negative function $f\left(t\right)=\{\begin{array}{l}\frac{2}{5}{e}^{-2t/5},t\ge 0\\ 0t<0\end{array}$ is a probability density function.

(b)

To determine

To calculate: The value of $P\left(0\le x\le 4\right)$ for $f\left(t\right)=\{\begin{array}{l}\frac{2}{5}{e}^{-2t/5},t\ge 0\\ 0t<0\end{array}$.

(c)

To determine

The value of $E\left(x\right)$ for $f\left(t\right)=\{\begin{array}{l}\frac{2}{5}{e}^{-2t/5},t\ge 0\\ 0t<0\end{array}$.