6.2. Customer accounts receivable at Smith Company are classified each month according to 0: Current 1: 30 to 60 days past due 2: 60 to 90 days past due 3: Over 90 days past due Consider a particular customer account and suppose that it evolves month to month as a Markov chain {X } whose transition probability matrix is

Suppose that a certain customer's account is now in state 1: 30 to 60 days past due. What is the probability that this account will be paid (and thereby enter state 0: Current) before it becomes over 90 days past due? That is, let T = min In ? 0; X = 0 or X,, = 3}. Determine Pr{XT = OIXO = 11.

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0 1 2 3 0 0.9 0.1 0 0 1 0.5 0 0.5 0 P = 2 0.3 0 0 0.7 3 || 0.2 0 0 0.8