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A government in a developed country is convinced that in order to win a national election, all it needs to do is ensure that the annual rate of inflation is between 1% and 3% at the time of the national election. The central bank in the country has informed the government that the annual force of inflation /, , recorded in each month r, can be modelled with the following equation, where Z, - N (1,1) : 1, = 0.951,_1 +0.0017, The current annual rate of inflation is 2.9%. (i] Find the distribution of /12- [5] (ii) Assuming that the government and the central bank are correct in their assertions, calculate the probability that the government will win the next national election in one year's time. [21 (iii) (a) Explain, with reasons, whether inflation in this model is mean-reverting. (b) Give an example of another financial quantity that would normally be considered to be mean-reverting. [3] [Total 10]