Questions l-Z ref to the following: Reference: Bart Sinclair. Machine Repair Model. OpenStax CNX. Jun 9, 2005 Creative Commons Attribution Liomse 1.0. Download for 'ee at 451 h :l/cnx or contents/S 6 flbedo -bd34-4c2 B-a2ec- 3Bded8e181 This material has been modified by Roberta Bloom, as permitted unda that license. A Markov chain can be used to model the status ofequipment, such as a machine used in a manufacturing process. Suppose that the possible states for the machine are Idle 82. awaiting work (1) Working on ajob/task (W) Broken (B) In Repair (R) The machine is monitored at regular intervals to determine its status; for use of interpretation in this problem we assume the status is monitored every hour. The transition matrix is shown below. I W B R I 0.05 0.93 0.02 0 T:W 0.10 0.86 0.04 0 B 0 0 0.80 0.20 R 0.5 0.1 0 0.4 1. Use the transition matrix to identify the following probabilities concerning the state of the machine one hour from now 3) Find the probability that the machine is working on a job one hour from now if the machine is idle now. b) Find the probability that the machine is idle one hour from now if the machine is working on ajob now. c) Find the probability that the machine is working on a job one hour from now if the machine is being repaired now. d) Find the probability that the machine is being repaired in one hour if it is broken now. 2. Perform the appropriate calculations using the transition matrix to nd the following probabilities concerning the state of the machine three hours from now. a) Find the probability that the machine is working on a job three hours from now if the machine is idle now. b) Find the probability that me machine is idle three hours from now if the machine is working on a job now. c) Find the probabiLity that the machine is working on a job three hours from now if the machine is being repaired now. d) Find the probability that the machine is being repaired in three hours if it is broken now. Teaching a computer music theory so that it can create music would be an extremely tedious task. You would have to teach chord structure, different musical styles. and so on. What if you could give the program examples of pieces you considered to be music and ask it, \"write something like that for me.\" This is essentially how our Markov chain would work. The principle behind Markov chains in music is to generate a probability table to determine what note should come next. By feeding the program an example piece of music, the program can analyze the piece and create a probability table to determine which notes are more likely follow a given note. With the probability transition matrix one can generate random notes that still has some musical structure to it. By constructing a similar matrix for beats or note durations, one can complete a Markov chain model for music generation. Source: Dec 18. 2008 Frank Chen. Textbook contmt produced by Frank Chen is liomsed under 5 WW license. Download for Em at Wm 95df-415a-b9nm 14fddd7o30a Q2." Modied by Roberta Bloom. as permitted under this license. The transition matrix below provides an example. The states are the notes A, A#.B.C.D.E.F.G.G#. The matrix shows the probability of die next note (column state), given the current note (row state). To generate computer created music, a computer program would randomly select the next note based on the previous note and the probabilities given in the transition matrix. A A# B C D E F G G# A 0.2 0 0.1 0 0.1 0.1 0 A# i 0 0 0 0 0 0 0 0.1 0.3 0 0.1 0 0 0 0.4 0.2 0.4 0 0 =D 0 0 0 0.25 0.25 0.5 0 0.1 0 0,1 0 0.2 0.2 0.1 0.1 0 0.2 D 0 0.2 0 0.6 0 0.2 0 0.2 0.4 0 0 0 0.2 0 Gt: 0 0 0.75 0 0 0.25 0 0 0 3) Find the probability for the next note, given the 4a) If the current note is A# (A-sharp) what does current note the transition matrix tell us about the next note? a. P[next note is A l Current note is G) : b. P(next note is G | current note is A) : 4b) If the next note is F. what do we know about 0. P(next note is C | current note is F) = the current note d. P(next note is E | current note is D) = Page