Question: Problem 6.

The useful life of a particular type of printer is measured by a random variable x with probability density function

\[f(x)=\left\{ \begin{matrix}

0.05{{e}^{-0.05x}}\quad if\quad x\ge 0 \\

0\quad if\quad x<0 \\

\end{matrix} \right.\]

where x denotes the number of months a randomly selected printer has been in use.

a. What is the probability that a randomly selected printer will last between 10 and 15 months?

b. What is the probability that a randomly selected printer will last less than 8 months?

c. What is the probability that a randomly selected printer will last longer than one year?

d. What is the expected life of a randomly selected printer?