Question

(3.) You are selling a particular model of used cellphone. Customers are hesitant to buy this model because it is known to sometimes have problems with the battery and sometimes with the CPU. Let's measure time in days and suppose that, given the phone is currently working, the probability of the battery failing the next day is 1/3 Likewise, the probability of the CPU failing the next day is 1/6 (and with probability 1/2 the phone continues to function properly). We can model the state of the phone as a 3-state DTMC. Suppose state 0 corresponds to CPU failure, state 1 corresponds to functioning normally, and state 2 corresponds to battery failure. (a) What is the transition matrix for the model? (b) Let's suppose that you don't know the state of the phone when you sell it to a customer because you have your supplier ship it directly to them. As a result when your customer receives the phone it might already have failed. Let aj be the probability that the phone is in state i when your customer receives it. What is the probability that it will be in each of the three different states, n days after they have received it? (c) Suppose the phone is working properly when your customer receives it. What is the probability distribution for the number of days before the phone fails (for any reason d) As an incentive you decide to offer you customers a free repair for the first time the phone malfunctions. If the cost of such repairs is $100 for a battery and $200 for a CPU, what is your expected cost per phone for offering this incentive in terms of the a,? (e) What is your expected cost per phone if you are certain that the phone will be working when your customer receives it?

Answer 1