The probability density function of the time to failure of an electronic component in a copier (in hours) is f left-parenthesis x right-parenthesis equals startfraction e superscript negative x divided by 1034 baseline over 1034endfraction for x greater-than 0. determine the probability that a) a component lasts more than 3000 hours before failure. (round the answer to 3 decimal places.) b) a component fails in the interval from 1000 to 2000 hours. (round the answer to 3 decimal places.) c) a component fails before 1000 hours. (round the answer to 3 decimal places.) d) determine the number of hours at which 10% of all components have failed. (round the answer to the nearest integer.)