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Over the last 100 years, families, private insurers, state governments and the federal government have all paid for mental health services. (a) describe how mental health financing has changed over the last 100years. Incude who paid for services and why different group either paid more or less over time. (b) describe the current balance between the state funding, federal funding, and private funding of mental health services. Specially, what types of care are paid for by federal dollars, state dollars and private dollars. (c) How did the affordable care act (aka obamacare) change funding of care for the seriously and persistently mentally ill and for more common but less severe cases of mental illness.

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?A Markov chain with state space {1, 2, 3} has transition probability matrix 0.6 0.3 0.1\\ P. = 0.3 0.3 0.4 0.4 0.1 0.5 (a) Is this Markov chain irreducible? Is the Markov chain recurrent or transient? Explain your answers. (b) What is the period of state 1? Hence deduce the period of the remaining states. Does this Markov chain have a limiting distribution? (c) Consider a general three-state Markov chain with transition matrix P11 P12 P13 P = P21 P22 P23 P31 P32 P33 Give an example of a specific set of probabilities p;; for which the Markov chain is not irreducible (there is no single right answer to this, of course !).Let {Xiji=1 36 be the sequence of continuous IIDRV with EXi = 40, Var Xi = 144, i = 1, ..., 36 and A36 Eil Xi = 36 (a) By using the Markov's inequality estimate P( A36