Kate keeps some of her money invested in technology and some invested in industrial stocks. At the end of a month during which the Dow Jones Industrial Average (a market indicator) goes up, she sells 10% of her industrial stocks and invests the money in technology stocks. At the end of a month during which the Dow goes down, she sells 20% of her technology stocks and invests the money in industrial stocks. Assume that each month the Dow goes up with probability 0.4 and that it goes down with probability 0.6, and that this is independent of what the Dow may have done in previous months. So, for a given share of industrial stock, the probability that it is sold at the end of a month and the money converted to technology stocks will be 0.4 .10 = 0.04 (the probability the Dow goes up multiplied times the percentage of industrial stock that is sold if the Dow goes up).Similarly, for a given share of technology stock, the probability that it is sold and the money reinvested in industrial stock is 0.6 .20 = 0.12 (the probability the Dow goes down times the 20% chance that this particular share will be sold if that happens).Based on this information, we can create a Markov Chain model of Kate's investments. This model is given below. (In other words, the following will be used as your transition matrix.)T = [0.88 0.120.04 0.96]Note: We can look at this 2-state Markov Chain as tracking a given dollar of Kate's investment. For example, a dollar invested in technology stocks has a 0.12 probability of being reinvested in industrial stocks the next month. Whereas a dollar invested in industrial stocks has a 0.04 probability of being shifted into technology stocks the next month. Based on this model, answer the following questions. (Give your answers correct to 3 decimal places.)(a) What is the probability that a dollar invested in technology stocks will be invested in technology stocks after 3 months?What is the probability that a dollar invested in industrial stocks will be invested in technology stocks after 3 months?(b) In the long run what fraction of Kate's money will be invested in technology stocks?