A South African government is convinced that to properly control the inflation of the country, all it needs to do is to ensure that the annual rate of inflation is between 3% and 6%. The reserve bank in the country has informed the government that the annual force of inflation It, recorded in each month t, can be modelled with the following equation It=0.8It1+0.01Zt where ZtN(1,1). The current annual rate of inflation is 6%. a) Assume that the rate of inflation is lognormally distributed, find the distribution of I12, the rate of inflation in month 12 . [9] HINT: Check geometric progression (from Grade 12) and statistics (from first year). b) Assuming that the government and the reserve bank are correct in their assertions, calculate the probability that the annual rate of inflation is between 3% and 6%. c) Assuming that the government and the reserve bank are correct in their assertions, calculate the probability that the annual rate of inflation is less than 3%. [3] A South African government is convinced that to properly control the inflation of the country, all it needs to do is to ensure that the annual rate of inflation is between 3% and 6%. The reserve bank in the country has informed the government that the annual force of inflation It, recorded in each month t, can be modelled with the following equation It=0.8It1+0.01Zt where ZtN(1,1). The current annual rate of inflation is 6%. a) Assume that the rate of inflation is lognormally distributed, find the distribution of I12, the rate of inflation in month 12 . [9] HINT: Check geometric progression (from Grade 12) and statistics (from first year). b) Assuming that the government and the reserve bank are correct in their assertions, calculate the probability that the annual rate of inflation is between 3% and 6%. c) Assuming that the government and the reserve bank are correct in their assertions, calculate the probability that the annual rate of inflation is less than 3%. [3]