Consider the linear model

Consider a Markov chain {Xn : n = 0, 1, 2, ...} with state space {1, 2, 3} and one-step transition probability matrix O NIH NIH P = O 0 O (a) Mark O or X: ( ) The Markov chain is irreducible. ( ) The Markov chain is aperiodic. ( ) The Markov chain is transient. ( ) The Markov chain is recurrent. ( ) The Markov chain is null recurrent. ( ) The Markov chain is ergodic. (b) Calculate P(X5 = 1/X2 = 1). (c) Find limn + P(Xn = 1/X2 = 1).Question 20 - Bivariate Distribution : Bivariate Distribution 1.0 0.8 06 04 0.2 0.0 0.0 0.6 0.8 Bivariate Distribution: Consider the experiment of picking a point (X,Y) from the right triangle above. The joint distribution of (X, Y) is given by: f(x, y) = c, for 0