6. Suppose the transition matrix for a Markov process isState AState BState A State B1{],1-PРwhere 0 < p < 1. So, for example, if the system is in state A at time 0 then the probabilityof being in state B at time 1 is p.(a) If the system is started in state A at time 0, what is the probability it is in state A at time2?(b) The transition matrix is stochastic. Is it regular? Why or why not?

P=paapbapabpbb=1-p1p0 Here, the column sum is one. Since the system is in state A at time 0…

Answered: Suppose the transition matrix for a…

A First Course in Probability (10th Edition)

10th Edition

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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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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.]
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2. Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix (1/2 1/2 0 0 1/7 0 3/7 3/7 1/3 1/3 1/3 0 0 2/3 1/6 1/6/ (a) Explain how you can tell this Markov chain has a limiting distribution and how you could compute it.
Suppose that a Markov chain with 3 states and with transition matrix P is in state 3 on the first observation. Which of the following expressions represents the probability that it will be in state 1 on the third observation? (A) the (3, 1) entry of P3 (B) the (1,3) entry of P3 (C) the (3, 1) entry of Pª (D) the (1,3) entry of P2 (E) the (3, 1) entry of P (F) the (1,3) entry of P4 (G) the (3, 1) entry of P2 (H) the (1,3) entry of P
A market demand has 3 possible states namely GOOD, NORMAL and BAD for each period. At each period there are 2 possible decisions for the manager as do nothing/ make promotion. The transition matrix of states regarding for possible decisions are given as below Pof do nothing GOOD NORMAL BAD GOOD 0.4 0.2 04 0.3 0.2 0.5 NORMAL 0.5 BAD 0.1 0.4 Pof make promotion GOOD NORMAL BAD 0.4 0.4 0.5 GOOD 0.2 NORMAL 04 0.1 BAD 0.3 0.4 0.3 It is known that the income for each period when the state in GOOD, NORMAL and BAD are 10000, 7000, 2000. Cost for do nothing is 0, and make promotion is 3000. a) Given at period 0 the state is NORMAL, estimate expected beneft obtain two periods when the sequence of decisions is do nothing, do nothing b) Given at period 0 the state is NORMAL, estimate expected beneft obtain two periods when the sequence of decisions is make promotion, make promotion

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