Basic descriptive samples

\fPoisson Regression. You are given the following information for a fitted generalized linear model (GLM): Response Variable: Claim count Response distribution: Poisson The link Function: log Parameter df B Intercept 1 Rating class Standard O Preferred -0.25 Miles driven (000) 0.035 Calculate the probability that a preferred driver who drives 15,000 miles submits at least 1 claims.Q.4 [12 marks] Give examples for Markov chains with the following properties. (a) The Markov chain has a state which is both transient and essential. [3 marks] (b) The Markov chain has a state which is null recurrent and aperiodic. [3 marks (c) The Markov chain has a stationary but not a limiting distribution? [3 marks] (d) The Markov chain has a stationary distribution which is not unique. 3 marks]A Markov chain with state space {1, 2, 3) has transition probability matrix 0.6 0.3 0.1\\ P. = 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. (b) What is the period of state 1? Hence deduce the period of the remaining states. Does this Markov chain have a limiting distribution? (c) Consider a general three-state Markov chain with transition matrix Pit P12 P13 P = P21 P22 P23 P31 P32 P33 Give an example of a specific set of probabilities paj for which the Markov chain is not irreducible (there is no single right answer to this, of course !)