6.0 The government has done a study of the flow of money among three types of financial institutions: banks, savings associations, and credit unions. We shall assume that the Markov assumptions are valid and model the monthly movement of money among the various institutions. Some recent data are: June Units in billions of dollars June amounts May totals bank savings credit other bank 10.0 4.5 1.5 3.6 19.6 savings 4.0 6.0 0.5 1.2 11.7 credit 2.0 3.0 2.4 13.4 other 4.0 2.0 4.8 12.3 May totals 20 15 10 12 57 For example, of the 20 billion dollars in banks during the month of May, half of it remained in banks for the month of June, and 2 out of the 20 billion left banks to be invested in credit unions during June. (a) Use the above data to estimate a Markov matrix. What would be the problems with such a model? (That is, be critical of the Markov assumption of the model.) (b) In the long-run, how much money would you expect to be in credit unions during any given month? (C) How much money would you expect to be in banks during August of the same year that the above data were collected? 1.5