(b) Given that the outcome state 1 has occurred, what is the probability that the next outcome of the experiment will be state 2?(c) If the initial-state distribution is given byState 154State 2find TX, the probability distribution of the system after one observation. The transition matrix for a Markov process is given byState123State 14T=21State 23(a) What does the entry a22- represent?O The conditional probability that the outcome state 2 will occur given that the outcome state 1 has occurred isO The conditional probability that the outcome state 1 will occur given that the outcome state 2 has occurred is -.O The conditional probability that the outcome state 1 will occur given that the outcome state 1 has occurred is .The conditional probability that the outcome state 2 will occur given that the outcome state 2 has occurred is-None of these are correct.(b) Given that the outcome state 1 has occurred, what is the probability that the next outcome of the experiment will be state 2?(c) If the initial-state distribution is given byState 1State 2find TX,, the probability distribution of the system after one observation.- In + lun

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Answered: The transition matrix for a Markov…

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...

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An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known:p3,2=0.35, p3, 3=0.25, p3,5=0.4p4,1=0.35, p4,3=0.4, p4,4=0.25p5,1=0.3, p5,2=0.2, p5,4=0.3, p5,5 = 0.2(a) Let T denote the transition matrix. Compute T3. Find the probability that if you start in state #3 you will be in state #5 after 3 steps. (b) Compute the matrix N = (I - Q)-1. Find the expected value for the number of steps prior to hitting an absorbing state if you start in state #3. (Hint: This will be the sum of one of the rows of N.) steps(c) Compute the matrix B = NR. Determine the probability that you eventually wind up in state #1 if you start in state #4.
1. 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…
Suppose that a production process changes state according to a Markov chain on [25] state space S = {0, 1, 2, 3} whose transition probability matrix is given by a) Determine the limiting distribution for the process. b) Suppose that states 0 and 1 are “in-control,” while states 2 and 3 are deemed “out-of-control.” In the long run, what fraction of time is the process out-of-control?
A study of armed robbers yielded the approximate transition probability matrix shown below. The matrix gives the probability that a robber currents free, on probation, or in jail would, over a period of a year, make a transition to one of the states. То From Free Probation Jail Free 0.7 0.2 0.1 Probation 0.3 0.5 0.2 Jail 0.0 0.1 0.9 Assuming that transitions are recorded at the end of each one-year period: i) For a robber who is now free, what is the expected number of years before going to jail? ii) What proportion of time can a robber expect to spend in jail? [Note: You may consider maximum four transitions as equivalent to that of steady state if you like.]
If she made the last free throw, then her probability of making the next one is 0.7. On the other hand, If she missed the last free throw, then her probability of making the next one is 0.2. Assume that state 1 is Makes the Free Throw and that state 2 is Misses the Free Throw. (1) Find the transition matrix for this Markov process. %3D
Given the transition matrix of a Markov process, what is the probability of going to state 3 from state 1 after 3 steps?
Consider the mouse in the maze shown to the right that includes "one-way" doors. Show that q (also given to the right), is a steady state vector for the associated Markov chain, and interpret this result in terms of the mouse's travels through the maze. To show that q is a steady-state vector for the Markov chain, first find the transition matrix. The transition matrix is P= 0. (Type integers or simplified fractions for any values in the matrix.) 4 2 3 5 6 q= 0
Which of the following best describes the long-run probabilities of a Markov chain {Xn: n = 0, 1, 2, ...}? O the probabilities of eventually returning to a state having previously been in that state O the fraction of time the states are repeated on the next step O the fraction of the time being in the various states in the long run O the probabilities of starting in the various states • Previous Not saved Simpfun
For the following Markov models: a ito dove b) find the stationary probability distribution on paper, SUre 5A An ion channel can be in either open or closed state. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. 5B An individual can be either susceptible or infected, the probability of infection for a susceptible person is 0.05 per day, and the probability an infected person becoming susceptible is 0.12 per day. 5C The genotype of an organism can be either normal (wild type) or mutant. Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring.
A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. At time t = 0, there are 100 people in state 1 and no people in the other state. state 1 Write the transition matrix for this system using the state vector v = state 2 T = Write the state vector for time t = 0. Vo Compute the state vectors for time t = 1 and t = 2. Vị = V2
At Suburban Community College, 30% of all business majors switched to another major the next semester, while the remaining 70% continued as business majors. Of all non-business majors, 10% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. HINT [See Example 1.] (Let 1 business majors, and 2 = non-business majors.) = Calculate the probability that a business major will no longer be a business major in two semesters' time.

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