Markov inequality

Problem 7.4 (10 points) A Markov chain Xo, X1, X2, ... with state space S = {1, 2,3, 4) has the following transition graph: 0.5 0.5 0.5 1 0.5 0.5 0.5 2 0.5 0.5 (a) Provide the transition matrix for the Markov chain. (b) Determine all recurrent and all transient states. (c) Determine all communication classes. Is the Markov chain irreducible? (d) Find the stationary distribution. (e) Can you say something about the limiting distribution of this Markov chain?Model: a right triangle. base and height can be modified. Three different views of triangle. View one displays lengths of sides. View two displays triangle graphically. View three logs changes in triangle state to file. A controller for view one, to modify triangle. No controller for other views.Determine if the following items represent an example of positive economics or normative economics. The richest 1% of Americans should pay more taxes than the rest of the 99%. O Positive Economics O Normative Economics A decrease in the supply of coconut will increase the price of German O Normative Economics chocolate cake, a good which requires coconut shavings as a key ingredient O Positive Economics The higher the minimum wage, the higher the price of goods and services Normative Economics is likely to bo. OO Positive Economics Social welfare spending in Sweden occupies too large a portion of the O Positive Economics national budget. O Normative Economics2. Recall that Markov's inequality says that if T' is a positive-valued random variable with mean E(T) then E(T) P(T > 1 ) 0 there holds P(1X - #| Ska) 21 - 1 That is. with probability at least 1 - 2. X stays within & standard deviations around its mean