The probability density function of the time to failure of an electronic component in a copier (in hours) is
f(x)=e−x/1000/1000
for x > 0. Determine the probability that a. A component lasts more than 3000 hours before failure. b. A component fails in the interval from 1000 to 2000 hours. c. A component fails before 1000 hours. d. The number of hours at which 10% of all components have failed.