Introduction and Purpose:

You have been introduced to a number of probability distributions. You have also learned that modeling any system (such as a communication system), needs the analysis of the input data. Random variables play an important role in the development of a model as they represent the input(s) to the modeled system. In order to use random variables in the modeling process, they need to be analyzed 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 the data sample in order to accept or refuse a certain hypothesis. A hypothesis, usually states that a specific data sample conforms to a certain probability distribution. The main purpose of this assignment is to find out via statistical analysis the probability distribution of the numerical data contained in a *.csv (comma separated) file.

Minimum objectives:

1) Read the ‘data.csv’ file into MATLAB using the csvread(‘filename’) function and save the data to a variable.

2) Compute the mean and standard deviation using your own custom functions and then verify these values by using the functions built into MATLAB.

3) Create a q-q plot of the data using the qqplot(x) function.

4) From the q-q plot, guess the probability distribution and then create data in a variable of that distribution type with around the same number of elements.

5) Complete a regression analysis and find out the equation of the line.

6) Report on all your findings.

Additional objectives:

1) Make a custom Chi-Square function in MATLAB.

2) Carry out a Chi-Square analysis of the data.

3) Report on all your findings.

Deliverables:

An individual report (times new roman pt 12, single lined spaced) which outlines your solution and the development of your MATLAB simulation. It must include as a minimum an explanation of your MATLAB implementation, screen captures of MATLAB plots, a plot of the sample distribution and any functions you have developed in appendices. The report must approximate the given structure: Title page, Contents page, List of figures, Introduction, MATLAB Implementation, Conclusions and Appendices (make sure all MATLAB code is clearly available in appendices).