Find the vector of stable probabilities for the Markov chain with this transition matrix. P%3D (A) [ ] (B) [4 %) (C) [ %] (D) [0 1] (E) [ %1 (F) [3 %13 ] (G) [½ % ] (H) [ %]
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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.Find the vector of stable probabilities for the Markov chain with this transition matrix. 1 P = (A) [½ ½] (B) [0 1] (C) [½ %] (D) [¼ ¾] (E) [¾ %] (F) [ % ] (G) [% % ] (H) [½ %]A Markov Chain has the transition matrix r-[% *]. P = and currently has state vector % % ]: What is the probability it will be in state 1 after two more stages (observations) of the process? (A) % (B) 0 (C) /2 (D) 24 (E) 12 (F) ¼ (G) 1 (H) 224
- Suppose that a Markov chain has transition probability matrix 1 2 1 P (1/2 1/2 2 1/4 3/4 (a) What is the long-run proportion of time that the chain is in state i, i = 1,2 ? 5. What should r2 be if it is desired to have the long-run average (b) Suppose that ri reward per unit time equal to 9?A Markov chain has the transition probability matrix 0.3 0.2 0.5 0.5 0.1 0.4 [0.5 0.2 0.3 Given the initial probabilities o1 = ¢2 = 0.2 and ø3 0.6, what is Pr (Xı = 3, X2 = 1)? %3DThe index model has been estimated for stocks A and B with the following results: RA = 0.03 + 0.8RM + eA. RB = 0.01 + 0.9RM + eB. σM = 0.35; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is A) 0384. B) 0.0406. C) 0.0882. D) 0.0772. E) 0.4000. 2) Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of A) the α of the asset. B) the β of the asset. C) the σ of the asset. D) the δ of the asset. Choose correct answer with justification.