The steady-state distribution vector X may be found by solving the vector equation T X = X together with the condition that the sum of the elements of X is 1.

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Chapter 9.2, Problem 29E

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The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

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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…

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Answer 2

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Chapter 9.2, Problem 29E

To determine

To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

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Answer 3

Question

Chapter 9.2, Problem 29E

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To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

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Answer 4

Question

Chapter 9.2, Problem 29E

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To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

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Answer 5

Chapter 9.2, Problem 29E

To determine

To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

Answer 6

Chapter 9.2, Problem 29E

To determine

To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

Answer 7

Chapter 9.2, Problem 29E

To determine

To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

Answer 8

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Answer 11

Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

The steady-state distribution vector X may be found by solving the vector equation T X = X together with the condition that the sum of the elements of X is 1.

Solution Summary: The author explains that the steady-state distribution vector X can be found by solving the vector equation TX=X with the condition that sum of the elements of is 1.

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The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

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Chapter 9 Solutions

The steady-state distribution vector X may be found by solving the vector equation T X = X together with the condition that the sum of the elements of X is 1.

Solution Summary: The author explains that the steady-state distribution vector X can be found by solving the vector equation TX=X with the condition that sum of the elements of is 1.

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To show: The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

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Chapter 9 Solutions

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The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.