The probability density function o4-8. the probability density function of the time to failureof an electronic component in a copier (in hours) is f(x)for determine the probability that(a) a component lasts more than 3000 hours before failure.(b) a component fails in the interval from 1000 to 2000hours.(c) a component fails before 1000 hours.(d) determine the number of hours at which 10% of all components have failed. use the continuous random variable way of doing this problem. with integration. f 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 1006 baseline over 1006endfraction 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.) .051 b) a component fails in the interval from 1000 to 2000 hours. (round the answer to 3 decimal places.) .233 c) a component fails before 1000 hours. (round the answer to 3 decimal places.) .630 d) determine the number of hours at which 10% of all components have failed. (round the answer to the nearest integer.)