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Q3: Vending machine A vending machine can be in two states, (0=working, 1=out of order). If the machine is working on a particular day it will be out of order with probability 6 on the next day. If the machine is out of order on a particular day then the probability that it will be working the next da}r is qr. a. Write down the one step transition probability matrix for the vending machine. [4 marks] b. Assume the machine is Working on Monday. What is the probability that the machine will remain working on all of 'Diesday, Wednesday and Thursday? [2 marks] 0. Assume the machine is working on Monday. What is the probability that the machine Will be working on Thursday? [4 marks] d. Calculate the equilibrium probabilities for the states of the vending machine. [5 marks] [Question total: 15] [[Assigmnent total: 32]]