The accounting department of a large firm is interested inmodeling the dynamics of its accounts receivable (that is, the money that isowed to it by its customers). when a charge sale occurs, a bill is sent out atthe end of the month. payment is due within thirty days, but may not occur inthat time. if no payment is received within six months of the billing date, theamount is classifed as a bad debt. thus, an individual account is described byits age in months, or by "paid", or "bad debt". for numerical values, assumethat the probability that the payment is made in the first month is 0.8 anddeclines by 0.1 each additional month. that is, the probability it is paid in thesecond month is 0.7, in the third month is 0.6, and so on.(a) formulate the terminating markov chain that describes the debt payment.(b) what is the probability that a bill that is not paid within the thirty-dayperiod will never be paid? (c) what is the probability that a bill will reach the point where it has gonethree months without being paid?