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For each of the following statements, enterT if the statement is true, enter F is the statement is false. DO NOT ENTER "True" or 'False". (a) If a branching process (2,) with 29 = 1 has offspring distribution pg! 6(5) satisfying G'(1) = 1 then the extinction probability must be 1. (b) If a branching process (2,) with 20 = 1 has offspring distribution pgf 0(5) satisfying 6(0) = 0 then the extinction probability must be 1. r (c) Let C1 and C2 be two distinct communicating classes of a Markov chain. and suppose there are two particular states a and b such that a is in C1 and b is in C2 and a > b. Then for all states i in C1 and j in C2, 1' r j. (d) If a nite state space, irreducible Markov chain has a unique stationary distribution, then it has a limiting distribution which is equal to this stationary distribution. (e) A Markov chain with a nite state space must have at least one recurrent state. (0 If i, j are states in a Markov chain, i is recurrent and 1' leads to 1'. then j must lead to it (9) If S2 and S3 are the second and third arrival times in a rate A Poisson process then 1309253) = E(SZ)E(S3). (g) If X is an exponential random variable with parameter 1/2. then Pr(X > 2h) = a(h) as h -> 0. 0) If (N,) is a rate A Poisson process, and 0