Problem 2. Consider one specific type of John Deere mowers that Lowes sells. There is a war ranty on all mower rs that requires free replacement of any mower that fails before it is 3 years old Suppose that (1) 2% of all new mowers fail d fail during the second year of operation; and (3) 10% of all 2-year-old mowers fall during the third year. uring fodel the sells of the mowers using a stochastic process by defining the state variable and transition probability matrix. [5 pts (2) Which states are transient, and which are absorbing states? (5 pts) (3) What is the fraction of all mowers that Lowes will have to replace? [10 pts (4) Suppose that it costs Lowes $300 to replace a mower and Lowes sells 7,000 mowers per year. If Lowes reduced the warranty period to two years, how much would be saved? (10 pts)