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In a multiple decrements model described by time-homogeneous Markov chains with state space S = [A. D. W), with state A. D. and W referring respectively to alive. death. and withdrawn, exit time 7, to D has geometric distribution with intensity 4 > 0, whilst exit time 7, to W has geometric distribution with intensity 4, > 0. i.e., that is for / = 1, 2. P(T, =0) = (1 -dyA, for! = 1.2 .... Notice that each intensity 1,, with / = 1,2, plays the role as P(7, = 1), yielding the survival probability P(7, 2 () = (1 - 1,)-1. As the exit times 7, and 7, are latent variables, denote by ? the observed exit time and by & the exit indicator defined by 7 = min(71. 72) and 6= 1, TIXT: 0, TI > 72. Assume that 7, and 7: are independent. We are interested in estimating the intensity , and d, by considering a independent paired observations (1.6,), with / = 1,2, ... , #, of the observed exit times r, taking place at r and the corresponding reason of exits 6. Subject Observed Exit ID exit time indicator U AWN -- N - W - -0 0- Table 1: Observations (1. 6,). The likelihood function of the observations (n,6,), with / = 1, 2, ... . n, is given by (1) (a) Show that the distribution of the observed exit time r is given by P(r >n= (1-A). for / = 1.2. ... where the intensity d is defined by A = 4, + (1 - d,)