Question 2: a) Consider an embedded continuous-time Markov chain X(t) on {1,2,3} has generator matrix 1 2 3 2 1 1-2 0 G = 2 0-1 1 3 3/2 3/2 -3] Write R code to find the long-term proportion of time that the chain visit state 1. (5 marks) b) The time when claims are submitted for an insurance policy are modeled as a Poisson process. For such a process, assume that the average time between claims is 3 hours. In a 12-hour period, find the probability that a third claim occurs in the last 0.5 hours of the period using R code. (3 marks) 101 Question 2: a) Consider an embedded continuous-time Markov chain X(t) on {1,2,3} has generator matrix 1 2 3 2 1 1-2 0 G = 2 0-1 1 3 3/2 3/2 -3] Write R code to find the long-term proportion of time that the chain visit state 1. (5 marks) b) The time when claims are submitted for an insurance policy are modeled as a Poisson process. For such a process, assume that the average time between claims is 3 hours. In a 12-hour period, find the probability that a third claim occurs in the last 0.5 hours of the period using R code. (3 marks) 101