Question: The useful life of a particular type of printer is measured by a random variable X with probability density:

\[f\left( x \right)=\left\{ \begin{aligned} & 0.02{{e}^{-0.02x}}\,\,\,\,\,x\ge 0 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x<0 \\ \end{aligned} \right.\]

where x represents the number of months 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 that 1 year?

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