-1 Pi. Consider the setting of the example from the lectures with the birth-death chain. This is a Markov chain on N such that if the chain is currently in state i then it moves to state i + 1 with probability Pi; otherwise it moves to state i 1 with probability qi Let 1 V then pi E (0,5/12). Suppose that Xo 2V and let H denote the hitting time of state i. By using results from the lectures or otherwise determine whether the following are true or false: - P2v(H V we have Pi E (0,4/5) If we now have a population limit of 2V individuals (so that the stochastic matrix has P2V,2V = P2v and P2v.2V-1 92v) while all other probabilities remain the same, then with pi (0,1) for all i E {1, 2, ...,2V} then we must have that P2v(H V then pi E (0,5/12). Suppose that Xo 2V and let H denote the hitting time of state i. By using results from the lectures or otherwise determine whether the following are true or false: - P2v(H V we have Pi E (0,4/5) If we now have a population limit of 2V individuals (so that the stochastic matrix has P2V,2V = P2v and P2v.2V-1 92v) while all other probabilities remain the same, then with pi (0,1) for all i E {1, 2, ...,2V} then we must have that P2v(H