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maintenance (assume one month 30 days = 240 hours). 2. After inserting their card into an ATM, there are three types of transactions that customers may perform: deposit, withdrawal, and obtain account information. The bank believes that 50% of all customers start with a withdrawal, 40% start with a deposit, and the remainder start by requesting account information. After completing a transaction, 90% of the customers complete their business (obtain their card and leave); those who do not complete their business are equally likely to select one of the other two types of transactions (for example, if they just made a withdrawal and they do not complete their business, then they are equally likely next to select a deposit or request account information). This pattern continues until their business finally is completed. Suppose that we have the following additional information about how long a customer spends on each transaction. All times are modeled as exponentially distributed random variables. 1 transaction Decide on first transaction Withdrawal Deposit Account information expected time 30 seconds 1 minute 2 minutes 1 minute a) Derive a Markov process model capable of answering the questions below. Be sure to define your state space, time index and generator matrix. b) What is the probability that a customer takes longer than 4 minutes at the ATM ? Calculate a numerical result. c) Calculate the expected time a customer spends at the ATM. 3. A spacecraft is sent to observe uniter It is supposed to take pictures of Jupiter's