Product failure behavior. An article in Hotwire (Dec.

2002) discussed the length of time till failure of a product produced at Hewlett-Packard. At the end of the product’s lifetime, the time till failure is modeled using an exponential distribution with mean 500 thousand hours. In reliability jargon, this is known as the “wear-out” distribution for the product. During its normal (useful) life, assume the product’s time till failure is uniformly distributed over the range 100 thousand to 1 million hours.

a. At the end of the product’s lifetime, find the probability that the product fails before 800 thousand hours.

b. During its normal (useful) life, find the probability that the product fails before 800 thousand hours.

c. Show that the probability of the product failing before 830 thousand hours is approximately the same for both the normal (useful) life distribution and the wear-out distribution.