Chapter 9.2, Problem 25E

(a)

To determine

To calculate: The probability $P\left(t<2\right)$, for the probability density function $f\left(t\right)=\frac{1}{3}{e}^{-t/3}$ over the interval $\left[0,\infty \right)$

(b)

To determine

To calculate:

The probability $P\left(t\ge 2\right)$, for the probability density function $f\left(t\right)=\frac{1}{3}{e}^{-t/3}$ over the interval $\left[0,\infty \right)$.

(c)

To determine

To calculate: The probability $P\left(1<t<4\right)$, for the probability density function $f\left(t\right)=\frac{1}{3}{e}^{-t/3}$ over the interval $\left[0,\infty \right)$.

(d)

To determine

To calculate: The probability $P\left(t>3\right)$, for the probability density function $f\left(t\right)=\frac{1}{3}{e}^{-t/3}$ over the interval $\left[0,\infty \right)$.