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Matlab Implementation Graphs and codes and Analysis
Learning Outcomes of this Assessment
On completion of this assignment it is expected that the student will have a basic
understanding of the use of random variables, probability distributions and input analysis in
modelling communication systems, and their implementation in MATLAB.
Key Skills to be Assessed
Research methods – background research on basic statistics may be required – use of
interactive help in MATLAB and online
Programming – MATLAB scripting
Communication – Production of written report
Introduction and Purpose
In the lectures and tutorials you have been introduced to a number of probability
distributions. You have also learned that modelling any system (such as communication
systems), requires the analysis of the input data. Random variables play an important role
in the development of any model, as they represent the input(s) to the modelled system. In
order to use random variables in the modelling process, they need to be analysed and
tested to verify that they represent a close fit to the real-world input. In order to do that, a
‘Goodness of Fit’ test is applied to a data sample in order to accept or reject a certain
hypothesis. A hypothesis, in this context generally questions if a particular data sample
conforms to a certain probability distribution.
The purpose of this assignment is to determine via statistical analysis the probability
distributions of the numerical data contained in two *.csv (comma separated) files.
Scenario and advice
There are two data files on Blackboard, Data(a).csv and Data(b).csv. The files
have been logged by a communications device and represent the input to a system. In
order to determine the effects on the output of the system, we need to be able to determine
their probability distributions. If you read the files in a text editor, it should be apparent that
one maybe a continuous distribution and the other possibly a discrete distribution (however
the type of distributions are unknown. To resolve this it is suggested that you carry out the
following:Network Programming and Simulation Assignment 1 Brief
DTN – level 7 – Network Programming and Simulation February 2015
Minimum objectives (full implementation of the following functions are
required for a pass at 40% – verification of these functions using the Matlab
built in functions carry additional marks up to a total of 50%)
1. For both files, read them into MATLAB (one at a time) using the
csvread(‘filename’) function and save them to a vector. (Note: these are your
observed data sets) (mark weighting = 5%)
2. Calculate the mean and standard deviation using custom functions and then
verify you answers with the functions built into MATLAB. (mark weighting =
5%)
3. Create a q-q plot of the data sets using the qqplot(x) function (this should
help you to guess the data’s distribution) (mark weighting = 5%)
4. Guess a probability distribution (create a null hypothesis) and create two
datasets with approximately the same number of elements as the data
provided in the data files. (Note: these will be your expected datasets) (mark
weighting = 5%)
5. Create a custom Chi-Square function in MATLAB (please refer to lecture 3
for an example, a MATLAB function template is also available on
Blackboard) (mark weighting = 10%)
6. Carry out a Chi-Square analysis of both sets of data (reference tables are on
Blackboard) (mark weighting = 10%)
7. Complete a regression analysis (if appropriate) and determine the equation
of the line for both data sets (please refer to lecture 4 for an example) (mark
weighting = 10%)
8. For each step above report on all your findings and reference any material
you have used.
Additional objectives (these are required for additional marks 50% – 100%)
1. Using the results obtained above select a data distribution and sample it
using the students t distribution (please refer to slide 21 in lecture 2) (mark
weighting = 20%)
2. Demonstrate graphically how, as the number of degrees of freedom
increases, the student’s t distribution approximates the normal distribution
and plot the variance between the curves. (mark weighting = 20%)
3. Verify your findings in 6 above using the Kolmogorov-Smirnov test
(kstest(x)). (mark weighting = 10%)
4. For each step above report on all your findings and reference any material
you have used.
Deliverables
The following must be submitted by the date outlined above:
An individual report (times new roman pt 12, single lined spaced) that outlines your
solution and the development of your MATLAB simulation. It should include as a
minimum an explanation of your MATLAB implementation, screen captures of the
MATLAB plots, and also a summary of the input analysis including a plot of the
quantile-quantile graph, a plot of the sample distribution and any functions you have
developed in appendices. The report should approximate the following structure:
Title page, Contents page, List of figures, Introduction, MATLAB Implementation,
Input Analysis, Conclusions and Appendices (make sure all MATLAB code is
clearly available in the appendices)
Assessment Criteria
The assignment must be completed on your own. The assignment must be completed on
time. This report count for 20% of the total marks assigned to this module. In general the
following outlines how this assignment will be graded.
• Report structure, presentation and clarity [20%]
• Appropriate technical content and its interpretation 50% + 10% research
methods
• Evaluation and Conclusions [20%]
Feedback
Feedback will be provided within two (academic) working weeks in the form of an individual
written assessment of both the report and the developed MATLAB solution.
Handing in Work
Your work should be submitted electronically via Blackboard by the date shown above.
Information on how to do this is available via:
Note about Plagiarism
Your submitted assignment must be written in your own words. The rules of plagiarism are
clearly stated in your Student Handbook which you must consult. You are strongly advised
to take care to reference and acknowledge any material that is not your own work. In
particular, you must make sure that:
· Any sentences, including any definitions that are copied word for word are in
quotation marks and cite the source(s);
· Any figures copied include citations to sources;
· Any code that is taken from any source (text book, WWW, journals etc) is fully
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