Kindly solve the following statements please

2. A Markov chain with state space {1, 2, 3} has transition probability matrix 0.0 0.3 0.1 [0\": 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. (1)) What is the period of state 1? Hence deduce the period of the remaining states. Does this Markov chain have a limiting distribution? (0) Consider a general three-state Markov chain with transition matrix P11 P12 P13 1? = P21 332-2 1023 P31 P32 P33 Give an example of a specic set of probabilities PM for which the Markov chain is not irreducible (there is no single right answer to this, of course !). What is the difference between univariate data and bivariate data? Choose the correct answer below. O A. In univariate data, a single variable is measured on each individual. In bivariate data, two variables are measured on each individual. O B. In univariate data, there are only positive values and zeros. In bivariate data, there are positive values, negative values, and zeros. C. In univariate data, there is one mean. In bivariate data, there are two means. O D. In univariate data, the data are qualitative. In bivariate data, the data are quantitative.Problem 7.4 (10 points) A Markov chain X0,X1,X2,. . . with state space S = {1,21 3,4} has the following transition graph: (3) Provide the transition matrix for the Markov chain. (b) Determine all recurrent and all transient states. 2. Markov chain transitions P = [Pil = HI- AI- NI- HI- NI- AI- NI- AI- +1- Let Xi be distributed uniformly over the states {0, 1, 2} . Let (Xi) be a Markov chain with transition matrix ; thus, P(Xn+1=j [Xn= i) = Pi, i, j E {0, 1, 2 ).