The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x)= e^-x/100 /1000. 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. Determine the number of hours at which 10% of all components have failed.

e. Determine the cumulative distribution function for the distribution. Use the cumulative distribution function to determine the probability that a component lasts more than 3000 hours before failure.