Transition matrix

4. Consider a discrete-time Markov chain with the following probability transition matrix 0 0 P= I-T- VVO 0 0 1 Is it possible to choose values for ar and y so that the Markov chain has the following properties? In each case, state the values of a and y, or give a brief reason why it is not possible. (a) The Markov chain has period 2. (b) The Markov chain is reducible. UNNN (c) The Markov chain has at least one transient state. (d) The Markov chain has invariant distribution (1/4, 1/4, 1/4, 1/4).6. ( 6 pts ) Consider the following symmetric matrix: 1 1 A=1 11 1 1 1 Compute the spectral decomposition of A = QAQwhere Q is an orthogonal matrix and A a diagonal matrix.A stationary distribution of an m-state Markov chain is a probability vector q such that = q P, where P is the probability transition matrix. A Markov chain can have more than one stationary distribution. Identify all the stationary distributions that you can, for the 3-state Markov chain with transition probability matrix O O P Owl Does this Markov chain have a steady-state probability distribution ? 15 pointsQUESTION 8 Porter's Five Forces model is based on: O industrial organization economics. labor and demographic economics. business administration and business economics. environmental and ecological economics