Problem 4: A finite state machine has 3 states, labeled {1, 2, 3}. The input of this statemachine is a binary value; it can only be 0 or 1. The probability of the input being 0 is 0.4.(a) Plot the state transition diagram and find the transition probability matrix given that:. When the input is 1 the machine moves to the state above the current state (2 is above 1, 3is above 2, 1 is above 3).. When the input is 0 the machine moves to the state below the current state (1 is below 2, 2is below 3, 3 is below 1).These are the only two possible transitions.(b) If the process starts in state 1 (Xo = 1), what is the probability that it will be in state 2 after3 transitions (X3 = 2)?(c) If we know that the process starts in state 3 (Xo = 3), what are the 3 state probabilities aftertwo transitions (that is, at time k = 2)?

Given that a finite state machine has 3 states, labeled {1, 2, 3}. The input of this state machine…

Answered: Problem 4: A finite state machine has 3…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

What is the transition matrix from S, to S, given
A machine can be in one of four states: ‘running smoothly’ (state 1), ‘running but needs adjustment’ (state 2), ‘temporarily broken’ (state 3), and ‘destroyed’ (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine to…
A car rental company has two locations. Each week, 80% of the cars rented at location A are returned to location A and the rest location B. Of the cars rented at location B, 30% are returned to location B by the end of the week and the rest to location A. a. Make a transition diagram for this process. b. Write the transition matrix T for this process. cIf 50% of the company's cars start this week at location A, and 50% at location B, find the proportion of cars that will be at each location one week later Label your answers. d. Write and solve a system of equations to find the stable distribution (correct to 3 decimal places) for this Markov process. Show all calculations and label the row operations.
60. The following is the transition probability matrix of a Markov chain with states 1, 2, 3, 4 P= .4 .2 .25 .2 .3 .2 .1 .2 .2 .4 25 50 .1 .4 .3 If Xo = 1 (a) find the probability that state 3 is entered before state 4; (b) find the mean number of transitions until either state 3 or state 4 is entered.
40. A Markov Chain with 4 states is currently equally likely to be in states 3 and 2, but is 4 times as likely to be in state 1 as in 3, and is 2 times as likely to be in 4 as in 1. What is the state vector that describes this situation?
Milan.stt
What is the probability that those units in states 3 and 4 end up in each of the absorbing states?
29. In a fictional town, there are two restaurants, which we will call A and B for ease of reference. If someone eats at restaurant A on one day, there is a 76% chance they will eat there again tomorrow. And if someone eats at restaurant B on one day, there is a 82 % chance they will eat there again tomorrow. Which one of the transition matrices below correctly represents this situation? a) A B A 0.76 0.34 B 0.18 0.82 b) A B A 0.76 0.24 B 0.18 0.82 c) A B A 0.76 0.24 B 0.08 0.82 d) A B Main Content A 0.24 0.76 B 0.82 0.18 e) None of the above.
1

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS