A simple NCD system has four levels of discount 0%, 20%, 4-0, % and 60%. A new policyholder starts on 0% discount. At the end of each policy year, policyholders will change levels according to the following rules: 0 At the end of a claim-free year, a policyholder moves up one level or remains on the maximum discount. 0 At the end of a year in which exactly one claim was made, a policyholder drops back one level or remains at 0%. 0 At the end of a year in which more than one claim was made, a policyholder drops back to zero discount. For a particular policyholder in any year, the probability oclaim-freefree year is 170 , the . . . . 1 . . . . 1 probablllty of exactly one clalm IS 3 and the probablllty of more than one claim Is 10' (i) Write down the transition matrix for this time-homogeneous Markov chain. (ii) Calculate the 2-step transition probabilities from state i to state j. (iii) Explain the term \"time-homogeneous Markov chain\