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?Suppose that X0, X1, X2, ... form a Markov chain on the state space {1, 2}. Assume that P(X0 = 1) = P(X0 = 2) = 1/2 and that the matrix of transition probabilities for the chain has the following entries: Q11 = 1/2, Q12 = 1/2, Q21 = 1/3, Q22 = 2/3.(a) Find P(X2 = 1).(b) Find the conditional probability P(X2 = 1|X1 = 1).(c) Find the conditional probability P(X1 = 1|X2 = 1).(d) Find limn→∞ P(Xn = 1).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)? %3D
- The 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.If she made the last free throw, then her probability of making the next one is 0.7. On the other hand, If she missed the last free throw, then her probability of making the next one is 0.3. Assume that state 1 is Makes the Free Throw and that state 2 is Misses the Free Throw. (1) Find the transition matrix for this Markov process. P = (2) Find the two-step transition matrix P(2) for this Markov process. P(2) = ... (3) If she makes her first free throw, what is the probability that she makes the third one? (3) If she misses her first free throw, what is the probability that she makes the third one? ...