16.2-3. Consider the second version of the stock market model presented as an example in Sec. 16.2. Whether the stock goes up tomorrow depends upon whether it increased today and yesterday. If the stock increased today and yesterday, it will increase tomor- row with probability a1. If the stock increased today and decreased yesterday, it will increase tomorrow with probability a2. If the stock decreased today and increased yesterday, it will increase tomorrow with probability a3. Finally, if the stock decreased today and yes- terday, it will increase tomorrow with probability a4. (a) Construct the (one-step) transition matrix of the Markov chain. (b) Explain why the states used for this Markov chain cause the math- ematical denition of the Markovian property to hold even though what happens in the future (tomorrow) depends upon what hap- pened in the past (yesterday) as well as the present (today)