Question

4. (30 points) The printer at the CAEN lab works as follows. If it is working at the beginning of a day, it continues to work until the next day with probability 0.65, and it fails with probability 0.35 (assume that it works for the entire day and only has a probability of failing when it is turned off at the end of the day). The repairman is very efficient: if the printer has failed at the end of the day, he will come to fix it at the beginning of the next day. It takes exactly 3 days for the repairs, at the end of which the machine is as good as new. (a) (10 points) Model this as a Markov Chain. Make sure to clearly define your states and give the transition probability matrix (b) (10 points) For the Markov Chain above: draw the state transition diagram, specify the classes, determine whether they are transient or recurrent, determine the period of each class and write whether or not the chain is irreducible. (c) (10 points) It is Monday morning and the printer is working. You must decide whether to print your IOE 316 homework now or to wat Thursday morning to print it (assume that those are the only two options). You think that you will get no more than an 80 in the homework if you print it now. If you wait, you could ask your instructor for help and get a 100 if you tur on time. Moreover, if the printer is not working when you try to print it on Thursday morning, you must go to the commons to print it (your homework will be late, and it will be marked over 75 points). Given that you are risk neutral (e.g. you wish to maximize your expected homework grade), should you print your homework now? (show all your work to receive full marks).

Answer 1

:) 0.399 y 400 246 0 0269 13S 26