r each of the following write T (True) or F (False) (no explanation : (a) All nite state space irreducible continuoustime Markov chains have a unique iimiting probability distribution. (b) The counting process of a Poisson process, {N (t) : t 2 {l}, is a Birth and Death process. (c) Little's Law (I 2 Am) requires that the arrival times of customers forms a renewal process. ((1) A Birth and Death process is a special case of a continuoustime Markov chain. (e) Let {X (t)} be an irreducible positive recurrent continuoustime Markov chain. Fix a state 2', let X (0) 2 i and let 131(1), n 2 1, denote the consecutive times that X (t) re-visits state i. Then the point process {131.1(2) : n 2 1} denes a renewal process. (f) A state i for a continuoustime Markov chain {X (t) : t 2 0} is recurrent if and only if it is recurrent for its embedded discrete time Markov chain {ann 20}. (g) It is possible for a continuoustime Markov chain to be null recurrent while its embedded discrete-time Markov chain is positive recurrent. (h) If T33 denotes the return time to state j given that X (0) I j for a positive recurrent continuous-time Markov chain {X (t)}, then 1/E(Tjj) is the longrun rate that this Markov chain visits state 3'. (i) If an irreducible continuous-tune Markov chain does not have a probability solution to the Global Balance Equations, then the Markov chain must be transient. ( j) The Birth and Death Balance equations always have a probability solution