2. Suppose a transition diagram is given as follows: 1 2 50 3 1/2 1/4 1/2 4 6 7 1/4 1/2 For this chain, there are two recurrent classes R₁ = {6, 7} and R₂ = {1, 2, 5}, and one transient class R3 = {3, 4}. (a) Find the period of state 3 and the probability that, starting at state 3, the state 3 is eventually re-entered (i.e., f33). (b) Assuming X₁ = 3, find the probability that the chain gets absorbed in R₁. Xo (c) Assuming X₁ = 3, find the expected time (number of steps) until the chain gets absorbed in R₁ or R2. More specifically, let T be the absorption time, i.e., the first time the chain visits a state in R₁ or R2. We would like to find E[T|X0=3]. Note: there are missing transition probabilities for this chain, but no impact for your solution.
2. Suppose a transition diagram is given as follows: 1 2 50 3 1/2 1/4 1/2 4 6 7 1/4 1/2 For this chain, there are two recurrent classes R₁ = {6, 7} and R₂ = {1, 2, 5}, and one transient class R3 = {3, 4}. (a) Find the period of state 3 and the probability that, starting at state 3, the state 3 is eventually re-entered (i.e., f33). (b) Assuming X₁ = 3, find the probability that the chain gets absorbed in R₁. Xo (c) Assuming X₁ = 3, find the expected time (number of steps) until the chain gets absorbed in R₁ or R2. More specifically, let T be the absorption time, i.e., the first time the chain visits a state in R₁ or R2. We would like to find E[T|X0=3]. Note: there are missing transition probabilities for this chain, but no impact for your solution.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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![2. Suppose a transition diagram is given as follows:
2
1/2
3
1/4
1/2
1/4
7
1/2
For this chain, there are two recurrent classes R₁ = {6, 7} and R₂
one transient class R3 = {3, 4}.
=
{1, 2, 5}, and
(a) Find the period of state 3 and the probability that, starting at state 3, the
state 3 is eventually re-entered (i.e., f33).
(b) Assuming X₁ = 3, find the probability that the chain gets absorbed in R₁.
(c) Assuming X = 3, find the expected time (number of steps) until the chain
gets absorbed in R₁ or R2. More specifically, let T be the absorption time,
i.e., the first time the chain visits a state in R₁ or R2. We would like to find
E[T|X = 3].
Note: there are missing transition probabilities for this chain, but no impact for
your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd067b7c3-c14f-4ae4-9cdc-b3e221c51f9f%2Ff78d3508-c36d-436a-ad11-16845bc466fe%2Fzv5ty4i_processed.png&w=3840&q=75)
Transcribed Image Text:2. Suppose a transition diagram is given as follows:
2
1/2
3
1/4
1/2
1/4
7
1/2
For this chain, there are two recurrent classes R₁ = {6, 7} and R₂
one transient class R3 = {3, 4}.
=
{1, 2, 5}, and
(a) Find the period of state 3 and the probability that, starting at state 3, the
state 3 is eventually re-entered (i.e., f33).
(b) Assuming X₁ = 3, find the probability that the chain gets absorbed in R₁.
(c) Assuming X = 3, find the expected time (number of steps) until the chain
gets absorbed in R₁ or R2. More specifically, let T be the absorption time,
i.e., the first time the chain visits a state in R₁ or R2. We would like to find
E[T|X = 3].
Note: there are missing transition probabilities for this chain, but no impact for
your solution.
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VIEWStep 2: Determine the period of state 3 and the probability of starting at state 3, eventually return to 3
VIEWStep 3: Determine the probability that the chain gets absorbed in R1 if X0=3
VIEWStep 4: Determine the expected time (number of steps) until the chain gets absorbed in R1 or R2.
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