What (if any) are the steady state results for a group of 14 students? [10 marks]
The Cannon Hill furniture Company produces tables and chairs. Each table takes five hours of labor from the carpentry department and three hours of labor from the finishing department. Each chair requires three hours of carpentry and two hours of finishing. During the current week, 230 hours of carpentry time are available and 90 hours of finishing time. Each table produced gives a profit of £85 and each chair a profit of £55. How many chairs and tables should be made?
A very new European “Rapid Reaction Force for Fire” has been created today and begins operation between three Countries “A”, “B” and “C”. It’s main resource is a super aircraft “Funderbird2” with a massive water cannon that even carries a small mini-submarine for fighting fires at sea. Unfortunately, it can only be in one Country at a time.
What is the matrix representation of this problem? [5 marks]
The probabilities of going to a fire in another Country, given that the force are in a given Country to begin with, are shown on the sketch above (any resemblance to any particular Country or Nation is purely coincidence and not intended). The probabilities were obtained as a weekly average using statistics for fires over many recorded weeks.
When will the plane take up permanent residence in one Country? [15 marks]
[Total 20 marks for this question]
5
0.1
A
0.5
0.1
0.3
B C
0.05
Figure 3. State diagram for Question 3.
For the state diagram shown on Figure 3 the initial state is ‘C’ and the time steps are days. Find the following:
i) Find the stochastic transitional probability matrix
[5 marks for this part]
ii) Find the probability of being in state ‘C’ after two time steps
[5 marks for this part]
iii) What is the steady state probability of being in state ‘A’?
[8 marks for this part]
iv) What is the steady state probability of being in either state ‘B’
OR
state ‘C’?
[2 marks for this part]
[Total 20 marks for this question]
Plagiarism
The use of work produced for another purpose by you, working alone or with others, must be acknowledged.
Copying from the works of another person (including Internet sources) constitutes plagiarism, which is an offence within the University’s regulations. Brief quotations from the published or unpublished works of another person, suitably attributed, are acceptable. You must always use your own words except when using properly referenced quotations.
You are advised when taking notes from books or other sources to make notes in your own words, in a selective and critical way.
General Criteria
In grading your work we will be assessing the extent to which it matches the criteria attached. The criteria are not of equal importance, but it is not possible to ascribe an exact weighting to each. What follows is intended as a general guide to the standards.
1. Severe weakness in understanding the issues/arguments/theory is likely to result in a mark of less than 40%.
2. Thorough coverage of the relevant material, with statements supported by data, evidence, literature or examples, is necessary to gain 52% or above.
3. Work which is disorganised with points randomly ordered is unlikely to gain more than 48%.
4. A logical, well-explained argument, combined with other good characteristics is usually necessary to obtain 75%.
5. Fluent grammatical expression is important for expressing ideas clearly. Errors in this area are likely to lead to a reduction in marks.
4
|
Grade
|
Relevance
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Knowledge
|
Analysis
|
Argument & Structure
|
Originality
|
Presentation
|
|
|
20%
|
20%
|
15%
|
20%
|
15%
|
10%
|
|
70 – 100%
|
Directly relevant to title. Able to address the implications, assumptions and nuances of the title.
Relevance to practice is thoroughly and explicitly addressed.
|
Makes effective use of a comprehensive range of theory and practice knowledge.
Demonstrates ability in the manipulation and transfer of subject material to demonstrate a solid understanding of the issues in both theory and practice.
|
A comprehensive analysis of the material resulting in clear and illuminating conclusions.
|
Coherent and logically structured, making creative use of an appropriate mode of argument and/or theoretical model.
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Distinctive work showing independent thought and critical engagement with alternative views.
|
A very well written answer with standard spelling and syntax.
Style is lucid and resourceful with an appropriate bibliographical apparatus.
|
|
60-69%
|
Directly relevant to title.
Is able to demonstrate effective practice relevance.
|
Makes effective use of good theory and practice knowledge.
Manipulates and transfers some material to demonstrate a clear grasp of the themes, questions and issues in theory and practice.
|
Good analysis of the material resulting in clear and logical conclusions.
|
Generally coherent and logically constructed.
Uses an appropriate mode of argument or theoretical model.
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Contains some distinctive or independent thinking.
Beginning to formulate an independent position
|
Well written with standard spelling and syntax.
Style is lucid utilising an appropriate format and bibliographical apparatus.
|
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50-59%
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Generally addresses the title, sometimes addresses irrelevant issues.
Relevance to practice effectively addressed, may be implicit in places.
|
Adequate knowledge of a fair range of relevant theoretical and practice related material with evidence of an appreciation of its significance.
|
Adequate analytical treatment, with occasional descriptive or narrative passages which lack clear analytical purpose.
Conclusions are clear.
|
Adequate attempt to construct a coherent argument, but may suffer loss of focus and consistency.
Issues at stake may lack clarity or theoretical models couched in simplistic terms.
|
Sound work which expresses a personal position, often in broad terms and tends towards uncritical conformity to one or more standard views of the topic.
|
Competently written with only minor lapses from standard spelling and syntax.
Style is readable with acceptable format and bibliographical status.
|
|
41-49%
|
Some degree of irrelevance to the title.
Superficial consideration of the issues.
Relevance to practice tends towards superficiality and is largely implicit.
|
Adequate knowledge of a limited range of relevant theoretical and practice related material with intermittent evidence of an appreciation of its significance.
|
Evidence of analytical ability.
Intermittent passages of descriptive or narrative material which lack clear analytical purpose.
Conclusions are not always clear and logical.
|
Some attempt to construct an argument is evident but it lacks sufficient clarity and coherence.
Issues at stake are only vaguely stated.
|
Largely derivative.
Attempts to present a personal view, but only in broad terms.
Is largely uncritical and conforms to one or more standard views.
|
Generally competent writing although intermittent lapses from standard syntax and spelling and pose occasional obstacles for the reader.
Format and bibliography is generally error free and acceptable.
|
|
40%
|
Some degree of irrelevance to the title is common.
Only the most obvious issues are addressed at a superficial level and in unchallenging terms.
Relevance to practice is superficially addressed and rarely made explicit
|
Basic understanding of a limited range of relevant theoretical and practice related material.
|
Largely descriptive or narrative in style with limited evidence of analytical capability.
Conclusions are not always clear or logical
|
A basic argument is evident but tends to be supported by assertion and lacks proper development.
Coherence and clarity are evident only intermittently
|
Largely derivative.
No personal view is adequately formulated
Wholly uncritical and conforming to one or more standard views.
|
Style of presentation makes reading difficult.
Deficiencies in spelling, syntax, format or bibliographical apparatus impact significantly upon clarity.
|
|
0-39%
|
Relevance to the title is intermittent or missing.
The topic is reduced to its vaguest and least challenging terms.
Relevance to practice is barely considered or not at all.
|
A limited understanding of a narrow range of relevant theoretical and practice related material or a lack of basic knowledge in either or both theory and practice necessary for an understanding of the topic
|
Heavy dependence on description and/or narrative.
Paraphrase is common.
Evidence of analysis is lacking.
Clear and logical conclusions are sparse
|
Little evidence of coherent argument.
There is a lack of development and the work may be repetitive and/or thin.
|
Almost wholly derivative.
The writer’s contribution rarely goes beyond simplifying paraphrase.
No evidence of personal thought.
|
Poorly written with numerous deficiencies in syntax, spelling, expression and presentation.
The writer may achieve clarity (if at all) only by using simplistic or repetitious style.
|
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mathgirl
math_assignment.docx
