Function of Random Variable
In this project we will perform engineering analysis. simulation. and comparison using the function of random variable technique.
In medical imaging such as computer tomography. the relation between detector readings Y and body absorptivity X follows a Y = ex law.
Requirements:
a) Let X : N(p. : theoretically derive the pdf of Y.
b) Develop a program (use any computer language you feel comfortable) to
o Generate one million samples for random variable U that is uniformly distributed between 0 and I.
o Transform these samples to samples of random variable X that Cottons normal distribution with mean p and variance a-. (you first need to derive a function for this conversion using the method similar to Example 32-6 in textbook)
o Transform the samples of random variable X to samples of Y using Y = ex law.
o Plot histograms of U. X. and Y.
o Compare the probability density function of U. X. and Y with the histograms of U. X. and Y.
c) Write a project report.
Other Requirements:
- Due. 7.10PM April 30 701C
- Write a report (maximum 5 pages) including the following, sections: Abstract. Introduction. Theoretical Analysis (pdf of 'Y and function that transforms uniform random variable to Gaussian random variable). Simulations and results. Conclusions. References, and Appendix (source codes).
- Comment your codes and attach it to your report.
- Follow IEEE conference paper format (US letter). The template could be found at blip•//www jeerorgfronfereneetrventsfconferrncesiptthlishiRritemplAte. hlml
- When cite from reference, use your own words based on your understanding.flgt and oasts is absolutely unacceotabk.
- The project report must be submitted on time and in class only. Work submitted in mailbox or slipped under the door will NCYT be accepted. Late work will NOT be accepted. except in real emergencies beyond the control of the student.
- No incomplete grade will be given to the project.
- Make sure your submission is a product of your own effort. Cheating will NOT be tolerated.