Spare line replacement units (LRU). The Department of U.S. Defense Reliability Analysis Center publishes Selected Topics in Assurance Related Technologies

(START) sheets to help improve the quality of manufactured components and systems. One START sheet, titled

“Application of the Poisson Distribution” (Vol. 9, No. 1, 2002), focuses on a spare line replacement unit (LRU). The number of LRUs that fail in any 10,000-hour period is assumed to follow a Poisson distribution with a mean of 2.1.

a. Find the probability that there are no LRU failures during the next 10,000 hours of operation.

b. Find the probability that there are at least one LRU failures during the next 10,000 hours of operation.