[SOLVED] math statistic BeijingDublin International College

BeijingDublin International College

SEMESTER I RESIT EXAMINATION20172018
School of Computer Science
BDIC Final Exam COMP3014J Performance of Computer Systems
HEAD OF SCHOOL: Padraig Cunningham MODULE COORDINATOR: Lina Xu
Time Allowed: 120 minutes
Instructions for Candidates
All questions carry equal marks. The distribution of marks in the right margin shown as a percentage gives an approximate indication of the relative importance of each part of the question.
BJUT Student ID:UCD Student ID:
I have read and clearly understand the Examination Rules of both Beijing University of Technology and University College Dublin. I am aware of the Punishment for Violating the Rules of Beijing University of Technology andor University College Dublin. I hereby promise to abide by the relevant rules and regulations by not giving or receiving any help during the exam. If caught violating the rules, I accept the punishment thereof.
Honesty Pledge: Signature
Instructions for Invigilators
Nonprogrammable calculators are permitted.
No roughwork paper is to be provided for candidates.

BDIC Semester One Academic Year 20172018
Question 1: General Theories on Performance
a. Whatarethethreecommonperformanceevaluationtechniquesandwhentouse them? Talk a little bit about their advantages and disadvantages. 7 Marks
b. Inthepapergroupreadingassignment,whatisthesystemdescribedyourpaper? What evaluation methods, workload and metrics were used? 8 Marks
c. In simulation, random number generation is open required. LinearCongruential Generators are the popular ones that can be applied efficiently. Explain how can you obtain a full period generator. 5 Marks
Question 2: Workload Characterization
a. Whatarethedifferencesbetweenfactorsandparameters?Presenttheanswerin your own words and also give some examples for both. 5 Marks
b. Consideraworkloadwithfivecomponentsandtwoparameters.TheCPUtimeand the number of disk IOs were measured for five programs. The parameter values after scaling are as shown in Table below. Based on the information given in the table, among all the other four programs, which one has the most similarity as A?
8 Marks
Obtained score
20
Obtained score
20
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So, since the nondiagonal elements in this covariance matrix are positive, we should expect that both the x and y variable increase together.
BDIC Semester One Academic Year 20172018
Step 4: Calculate the eigenvectors and eigenvalues of the
covariance matrix
c. What is the main advantages to apply Principal Component Analysis PCA when
Since the covariance matrix is square, we can calculate the eigenvectors and
analysing high dimensional dataset? Given the following eigenvalues and
eigenvalues for this matrix. These are rather important, as they tell us useful eigenvinefcotromrast,iownhabicohutvoeucrtdoartais.Ithweillpsrhionwciypoluewchoymsopoonn.eInthoefmtheaentdimaeta,hserte?
7 Marks
It is important to notice that these eigenvectors are both unit eigenvectors ie. their lengths are both 1. This is very important for PCA, but luckily, most maths packages, when asked for eigenvectors, will give you unit eigenvectors.
are the eigenvectors and eigenvalues:
eigenvalues .0490833989
1.28402771 eigenvectors .735178656 .677873399
.677873399 .735178656
So what do they mean? If you look at the plot of the data in Figure 3.2 then you can see how the data has quite a strong pattern. As expected from the covariance matrix, they two variables do indeed increase together. On top of the data I have plotted both the eigenvectors as well. They appear as diagonal
Question 3: Summarize Measured Data dotted lines on the plot. As stated in the eigenvector section, they are perpen
Obtained score
30
dicular to each other. But, more importantly, they provide us with information
about the patterns in the data. See how one of the eigenvectors goes through
the middle of the points, like drawing a line of best fit? That eigenvector is
showing us how these two data sets are related along that line. The second
a. Ingeneral,whatareQQplotsusedfor?Whatisthemainadvantageofqqplots
eigenvector gives us the other, less important, pattern in the data, that all the
over histograms? 5 Marks
points follow the main line, but are off to the side of the main line by some amount.
So, by this process of taking the eigenvectors of the covariance matrix, we have been able to extract lines that characterise the data. The rest of the steps involve transforming the data so that it is expressed in terms of them lines.
14
b. Dothefollowingvaluescomefromanormaldistribution?Demonstratetheprocess. 7.19, 6.31, 5.89, 4.5, 3.77, 4.25, 5.19, 5.79, 6.79. 14 Marks
c. A random sample of 225 first year statistics tutorials was selected from the past 5 years and the number of students absent from each one recorded. The results were: sample mean x 11.6 and standard deviation4.1 absences. Calculate the mean number of absences per tutorial over the past 5 years with 90 confidence.
7 Marks
d. Inlinearregression,whatisthedefinitionforcoefficientofdetermination?Whatit
means?
4 Marks
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BDIC Semester One Academic Year 20172018
Question 4: Queuing Model
a. MM1 model is a special case for birth and death model, where lkl, k0,1, and k, k1,2,. Deduce the following formula
L l providedl l
Where L is the mean number of customers in the system. Then use basic laws and relationships, derive the mean wait in the system W. 12 Marks
b. Customers for a bank arrive in a usual MM1 system, with an arrival rate i and service rate i, where i is the existing customers in the bank. If i for i0, 1, 2. ii1 for i0, 1, 2. Draw the Markov Chain diagram for this queue and derive the stationary probability pi in this chain. 18 Marks
Obtained score
30
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Appendix :
BDIC Semester One Academic Year 20172018
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BDIC Semester One Academic Year 20172018
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