Find the steady-state probability vector for the stochastic matrix P. [0.9 0.3 0.2] P = 0.1 0.6 0.3 0 0.1 0.5
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![Find the steady-state probability vector for the stochastic matrix P.
[0.9 0.3 0.2]
P = 0.1 0.6 0.3
0 0.1 0.5
Select one:
A. 3
35 3100 13 1353 13
25
25
D.matrix ((17)(5)(1))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F714cf023-bf93-4290-a149-c98da4567ece%2Fc59460b6-5cac-4e2f-a119-fbf3085861f7%2Ffo5zo7_processed.png&w=3840&q=75)
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- Suppose two forces Red and Blue, with Red having a starting force = 2, and Blue having a starting force = 1. Engage in a stochastic Lanchester battle assuming square law, in a fight-to-the-finish, with Red a = 0.01 casualties per minute, and Blue b = 0.03 casualties per minute. (a) What is the expected time of the first casualty?(b) What is the probability that there are no casualties in the first 20 minutes?(c) What is the expected number of Red survivors and the expected length of the battle?Consider a simple model of the hunting behaviour of a fox. In a single day, the fox catches either 0 or 1 rabbits, with probabilities 0.3 and 0.7, respectively. The outcome of hunting on day m is independent of all other days.We describe this system through a discrete-time, discrete-state stochastic process R(m), where R is the total number of rabbits caught between the end of day 0 (defining a starting point of our observation) and the end of day m. m = 0,1,2,3... is thus a discrete time parameter, and R(0) = 0 by definition (a) It can be shown that pr(m) – the probability of catching R = r rabbits in m days – is given by a binomial distribution (see Appendix A.2.1). Here, m is the number of “trials”, r the number of successes and q = 0.7 the probability of success. Hence give expressions for:i The mean number of rabbits caught after m days. ii The standard deviation of the total number rabbits caught after m days. iii The standard deviation of the mean number of rabbits caught per day…A laboratory animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one foodon one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%. a. What is the stochastic matrix for this situation? b. If the animal chooses food #1 on an initial trial, what is the probability that it will choose food #2 on the second trial after the initial trial?
- why is the covariance of a deterministic and a stochastic process 0? This relats to Arithmetic Bronian MotionCommuters can get into town by car or bus. Surveys have shown that, for those taking their car on a particular day, 20% take their car the next day and 80% take a bus. Also, for those taking a bus on a particular day, 50% take their car the next day and 50% take a bus. Assume you are starting on a Monday. a) Write a stochastic matrix A and label the states. b) What percentage of the people who initially drive their own car will take their car on Tuesday? c)What percentage of people who initially drive their own car will take their car on Wednesday? d)What percentage of people who initially drive their own car will take their car on Thursday. e)In the long run, what percentage of the people who initially drive their own car will take their car on any particular day? f)What is the stable matrix? What is the stable distribution? g) In the long run, what percentage of the people take their car on a particular day? h) In the long run, what percentage of the people take the bus…In the B&K model of Example 18.5-1, suppose that the interarrival time at the checkout area is exponential with mean 5 minutes and that the checkout time per customer is also exponential with mean 10 minutes. Suppose further that will add a fourth counter. Counters 1,2, and 3 will open based on increments of two customers and counter 4 will open when there are 7 or more in the store. (a) The steady-state probabilities, for all . (b) The probability that a fourth counter will be needed. (c) The average number of idle counters.
- On any given day, a student is either healthy or ill. Of the students who are healthy today, 95% will be healthy tomorrow. Of the students who are ill today, 55% will still be ill tomorrow. a. What is the stochastic matrix for this situation? b. Suppose 20% of the students are ill on Monday. What fraction or percentage of the students are likely to be ill on Tuesday? On Wednesday? c. If a student is healthy today, what is the probability that he or she will be healthy two days from now?If X and Y are independent Poisson random variables with E[X] = 3 and E[Y] = 2, what is P[ X = 2 | X + Y = 4 ]?"NEED HELP ASAP" For a certain group of states, it was observed that 60% of the Democratic governors were succeeded by Democrats and 40% by Republicans. Also, 20% of the Republican governors were succeeded by Democrats and 80% by Republicans. (a) Set up the 2×2 stochastic matrix with columns and rows labeled D and R that displays these transitions. (b) Compute A2 and A3. (c) Suppose that all the current governors are Democrats. Assuming that the current trend holds for three elections, what percent of the governors will then be Democrats? D R (a) The stochastic matrix is D nothing nothing R nothing nothing (b) A2= A3= (c) nothing% of the governors will be Democrats after three elections.
- Peter takes the course Basic Stochastic Processes this quarter on Tuesday, Thursday, and Friday. The classes start at 10:00 am. Peter is used to work until late in the night and consequently, he sometimes misses the class. His attendance behaviour is such that he attends class depending only on whether or not he went to the latest class. If he attended class one day, then he will go to class next time it meets with probability 1/2. If he did not go to one class, then he will go to the next class with probability 3/4. Describe the Markov chain that models Peter’s attendance. What is the probability that he will attend class on Thursday if he went to class on Friday?Peter takes the course Basic Stochastic Processes this quarter on Tuesday, Thursday, and Friday. The classes start at 10:00 am. Peter is used to work until late in the night and consequently, he sometimes misses the class. His attendance behaviour is such that he attends class depending only on whether or not he went to the latest class. If he attended class one day, then he will go to class next time it meets with probability 1/2. If he did not go to one class, then he will go to the next class with probability 3/4. Suppose the course has 30 classes altogether. Give an estimate of the number of classes attended by Peter and explain it.If ? = [ 0.2 0.6 0.8 0.4 ] is the transition matrix for a regular Markov Chain, then the associated steady state vector is: a. ? = [ 3/7 4/7 ] b. ? = [ 4/7 3/7 ] c. ? = [ 2/5 3/5 ] d. ? = [ 3/5 2/5 ] 19. If ? is a random variab
