math 632 004 hw04 - shawn zhongmath 632 004 hw04 shawn zhong total points 60 / 60 question 1 1...
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![Page 1: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/1.jpg)
Math 632 004 HW04Shawn Zhong
TOTAL POINTS
60 / 60
QUESTION 1
1 Problem 1 10 / 10
✓ - 0 pts Correct
- 2 pts (a) One wrong detailed balance distribution
- 4 pts (a) Both detailed balance distributions are
wrong
- 2 pts (b) Only asserted there are no additional
invariant distributions for the first Markov chain
without proof
- 2 pts (b) Did not find the other invariant distribution
for the second Markov chain
- 2 pts (b) Did not give the right result of one of the
Markov chain
- 4 pts (b) Did not give the right results of both
Markov chains
- 10 pts No work submitted
QUESTION 2
2 Problem 2 10 / 10
✓ - 0 pts Correct
- 2 pts Some minor arithmetic or other
computational errors
- 4 pts Setup the equations correctly but did not
solve them
- 7 pts Made some effort, but there are substantial
errors in the linear equations
- 10 pts No work submitted
QUESTION 3
3 Problem 3 10 / 10
✓ - 0 pts Correct
- 10 pts No work submitted
QUESTION 4
4 Problem 4: Durrett 1.56 10 / 10
✓ - 0 pts Correct
- 2 pts Some minor computational errors
- 4 pts The linear equations are set up, but there is
no attempt to solve them
- 7 pts There are substantial errors in the way the
linear equations are set up
- 10 pts No work submitted
QUESTION 5
5 Problem 5: Durrett 1.58 10 / 10
✓ - 0 pts Correct
- 2 pts (a) There are some mistakes in the transition
probabilities
- 2 pts (a) The transient or recurrent states are not
correctly identified
- 2 pts (b) The linear equations are not set up
correctly
- 2 pts (b) The linear equations are not solved
correctly
- 10 pts No work submitted.
QUESTION 6
6 Problem 6: Durrett 1.67 10 / 10
✓ - 0 pts Correct
- 2 pts (a) There are some mistakes in the transition
probabilities
- 2 pts (a) The transient or recurrent states are not
correctly identified
- 2 pts (b) The linear equations are not set up
correctly
- 2 pts (b) The linear equations are not solved
correctly
- 10 pts No work submitted
Page 1
![Page 2: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/2.jpg)
![Page 3: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/3.jpg)
![Page 4: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/4.jpg)
1 Problem 1 10 / 10
✓ - 0 pts Correct
- 2 pts (a) One wrong detailed balance distribution
- 4 pts (a) Both detailed balance distributions are wrong
- 2 pts (b) Only asserted there are no additional invariant distributions for the first Markov chain without proof
- 2 pts (b) Did not find the other invariant distribution for the second Markov chain
- 2 pts (b) Did not give the right result of one of the Markov chain
- 4 pts (b) Did not give the right results of both Markov chains
- 10 pts No work submitted
Page 4
![Page 5: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/5.jpg)
![Page 6: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/6.jpg)
2 Problem 2 10 / 10
✓ - 0 pts Correct
- 2 pts Some minor arithmetic or other computational errors
- 4 pts Setup the equations correctly but did not solve them
- 7 pts Made some effort, but there are substantial errors in the linear equations
- 10 pts No work submitted
Page 6
![Page 7: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/7.jpg)
![Page 8: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/8.jpg)
![Page 9: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/9.jpg)
3 Problem 3 10 / 10
✓ - 0 pts Correct
- 10 pts No work submitted
Page 9
![Page 10: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/10.jpg)
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4 Problem 4: Durrett 1.56 10 / 10
✓ - 0 pts Correct
- 2 pts Some minor computational errors
- 4 pts The linear equations are set up, but there is no attempt to solve them
- 7 pts There are substantial errors in the way the linear equations are set up
- 10 pts No work submitted
Page 11
![Page 12: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/12.jpg)
![Page 13: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/13.jpg)
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5 Problem 5: Durrett 1.58 10 / 10
✓ - 0 pts Correct
- 2 pts (a) There are some mistakes in the transition probabilities
- 2 pts (a) The transient or recurrent states are not correctly identified
- 2 pts (b) The linear equations are not set up correctly
- 2 pts (b) The linear equations are not solved correctly
- 10 pts No work submitted.
Page 14
![Page 15: Math 632 004 HW04 - Shawn ZhongMath 632 004 HW04 Shawn Zhong TOTAL POINTS 60 / 60 QUESTION 1 1 Problem 1 10 / 10 - 0 pts Correct - 2 pts (a) One wrong detailed balance distribution](https://reader036.vdocuments.net/reader036/viewer/2022071516/6139d3910051793c8c00b2fe/html5/thumbnails/15.jpg)
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6 Problem 6: Durrett 1.67 10 / 10
✓ - 0 pts Correct
- 2 pts (a) There are some mistakes in the transition probabilities
- 2 pts (a) The transient or recurrent states are not correctly identified
- 2 pts (b) The linear equations are not set up correctly
- 2 pts (b) The linear equations are not solved correctly
- 10 pts No work submitted
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