2. A manufacturer of laptop computers offers a one-year warranty. If the laptop computer fails for any reason during this period, it is replaced. The length of satisfactory service (years) is a random variable having the probability density function f (x) = 1 e - x / 2.6 2.6 x > 0 a) What percentage of the laptops will fail within the warranty period? ABCS b) Find the probability that one of these laptops will provide satisfactory service for up to 2 years. c) The manufacturing cost of a laptop computer is $100, and the profit per sale is $300. What is the effect of warranty replacement on profit? d) Calculate the mean life-time of the laptops