Consider a magnetic hard disk on which data is written as a string of ones and zeros. Because of the magnetic interaction, 1's cannot occur consecutively. In addition, it is assumed that no more than two zeros can be in a row. For example, queue 00101001 is possible, while queues 0001010 and 0110100 are impossible. After the first two characters are written to the hard disk, the process of writing new characters can be modelled as a stochastic process using the following transition diagram: 00 1 1-a 1 10 8 In the diagram, the nodes describe which characters were written to the queue last, and the arcs describe the transition probabilities when a new character is added to the queue. a.) Is the stochastic process described above Markov, time invariant, irreducible, aperiodic in the following cases = 0? = 1? 0 < a < 1? b.) In the range 0 < a < 1, calculate the entropy growth rate of the process as a function of a. When is the growth rate at its highest? (numerical solution is sufficient)