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Consider the following Markov chain with the following transition diagram on states {1, 2, 3} al- 2 CO 173 3 (a) Is this Markov chain irreducible? [1 marks] (b) Find the probability of the Markov chain to move to state 3 after two time steps, providing it starts in state 2. [3 marks]Problem 3. Consider the Markov chain shown in Figure 2. Figure 2: Problem 3 Markov chain 1. Let the initial distribution be Pr(A) : Pr(B) = 0.5. What is the probability distribution after one step? 2. What is the stationary distribution of the Markov chain? Problem 7.4 (10 points) A Markov chain X0,X1, X2, . . . with state space S = {1, 2, 3, 4} has the following transition graph: (a) Provide the transitiOn matrix fer the Markov chain. (13) Determine all recurrent and all transient states. Which of the following is an advantage of multivariate correlational research over bivariate correlational research? O Bivariate correlational studies help address internal validity, whereas multivariate correlational studies do not. Multivariate correlational studies establish covariance, whereas bivariate correlational studies do not. O Some multivariate correlational studies help to address temporal precedence, whereas bivariate correlational studies do not. Multivariate correlational studies help to address external validity, whereas bivariate correlational studies do not