2. We suggest a model for stock price prediction that takes into account consecutive day trends as influencing the price. You've noticed the following trend: If the stock has increased in price for the past two days then it will increase tomorrow with probability 90%; UU 90% U If the stock increased today but decreased yesterday then it will increase tomorrow with probability 60%; DU 60% U If the stock increased decreased today but increased yesterday then it will increase tomorrow with probability 50%; UD 5% U If the stock decreased both today and yesterday then it will increase tomorrow with probability 30%; DD 30% U % You can't represent this behaviour through Markov Chains to predict whether a stock will increase the next day. However, this problem is resolved if you consider the joint states of both tomorrow and oday. Let Bn be the chance that the stock will increase on day n and day n - 1. In be the chance that the stock will increase on day n but decrease on day n-1 Yn be the chance that the stock will decrease on day n but increase on day n - 1 Fn be the chance that the stock will decrease on day n and on day n - 1 . answer the following questions: (a) Construct linear equations for B2, T2, Y2 and F2 in terms of Bi, T, Y1 and Fi and use this to determine the transition matrix. (b) Determine all stable eigenvectors of the transition matrix and comment as to whether or not this stock is a good investment