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…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...

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1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2
There are two boxes. At first, each box contains one white ball and one black ball. At each step, we draw one ball from each box randomly and exchange them. If we set that State 1 = Box 1 contains no white balls, State 2= Box 1 contains one white ball, State 3 = Box 1 contains two white balls. 1. Find the transition matrix. Answer: 2. After 10 steps, what is the probability that box 1 contains two white balls? Answer: Submit Question
Suppose that Phone A has a 20% market share initially, with Phone B having an 80% market share. The transition matrix to the right represents customers who currently own phones A and B and the probability that they will upgrade to a new phone A or B. Use this transition matrix to find the share for each phone after the following upgrades. A B A 0.8 0.2 B 0.25 0.75 (a) First upgrade (b) Second upgrade (c) Third upgrade (a) With the first upgrade, Phone A has % of the market and Phone B has % of the market. (Round your answers to two decimal places as needed.)
state 1[.1 .1 .8 1. Consider the transition matrix P= state 2.5 5 0 state 3.7 0 3 a. Identify what the entry in row one, column three (the .8) represents: b. Find p (use your calculator. no work required): c. Identify what the entry in row two, column one of represents.
The weather in the Magical Land of Oz only depends on the weather from the previous day. There are four possible weather patters: Sunny, Raining, Foggy, and Hailing. The probability transition matrix is given 1: below. S R F H S 1 R 1/2 1/4 1/4 F 1/4 3/4 H 0 0 1/4 3/4 1. If it is Raining today, what is the weather forecast for tomorrow? 2. If it is Raining today, what is the weather forecast for a week from today? 3. If it is Raining today, what is the weather forecast for a year from today? 4. If it is Raining today, what is the weather forecast for ten years from today? 5. Find the stable state vector.
Ex. 17b-Section 4.2, Exercise 17b A k out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. Assume the components function independently of one another. In a 3 out of n system, in which each component has probability 0.4 of functioning, what is the smallest value of n needed so that the probability that the system functions is at least 0.4? Note: Your answer must be a whole number. The smallest value of n needed so that the probability that the system functions is at least 0.4=
the map below shows a one-way subway system starting from station 1. A passenger can go from each station to others with equal probability. so a passenger from station 1 can go any other station with probability of 1/4 since there are 14 remaining stationss. a passenger from station 11 can go to any of the remaining stations (12-15) with probability 1/4. what is the probability transition matrix?
Q4. Assume that only at the end of a year a person can change her cola preferences based on the following probability transition matrix - Pepsi, Coke, cola Turka, no cola.- (If a person becomes no cola drinker or cola Turka drinker, she would never change her preferences) ; Pepsi Coke 0,7 0,1 0,75 0,15 Turka No cola Pepsi Coke 0,15 0,5 0,5 0,5 Turka 1 No cola 1 a. What is the average number of years that a Pepsi drinker spends until she becomes either cola Turka drinker or no cola drinker? b. What fraction of Coke drinkers becomes no cola drinker eventually? c. What is the probability that a Pepsi drinker becomes Coke drinker before she becomes either cola Turka drinker or no cola drinker?
2. A manufacturer has a machine that, when operational at the beginning of a day, has a probability of 0.1 of breaking down sometime during the day. When this happens, the repair is done the next day and completed at the end of that day. The one-step transition matrix is obtained from Week 12 assignment Problem #3: State O-operational, state 1 – break down, state 3 -- repaired 0.9 0.1 0 0 0 1 0.9 0.1 0 P = (a) Use the approach described in Sec. 29.6 to find the µ¡¡ (the expected first passage time from state i to state j) for all i and j. Use these results to identify the expected number of full days that the machine will remain operational before the next breakdown after a repair is completed. (b) Now suppose that the machine already has gone 20 full days without a breakdown since the last repair was completed. How does the expected number of full days hereafter that the machine will remain operational before the next breakdown compare with the corresponding result from part (b) when…
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Consider the graph with 6 vertices given below and with resistances given by the numbers above each edge. As before, vertices 0 and 5 are absorbing. 3 4 -IN 2 1 3 4 4 th 5 (a) Calculate the total conductance at each vertex and the transition probabilities between each vertex. Write the transition matrix P. Find poo (b) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0? (c) What is the probability that a walker starting at vertex 3 is absorbed by vertex 5? (d) What is the expected number of times that a walker starting at vertex 1 will visit vertex 2?

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