ECE 413 Exams

Fall 2006

You may not take the Conflict Final Exam unless you actually have a conflict on the regular Final Exam. You must inform me if you have a conflict on the Final Exam, **and** provide me with a copy of your complete exam schedule so that if you have a conflict on the conflict exam as well, I can try to reschedule the Conflict Final Exam to a time when all conflictees can take the exam.

- You are allowed to bring TWO 8.5" by 11" sheets of notes to the exam;
both sides of the sheets can be used, but the exam is closed-book
and closed-notes otherwise.
Electronic devices (calculators, cellphones, pagers, laptops, etc.)
are neither necessary nor permitted.
- You are expected to know what is meant by
- a Bernoulli random variable with parameter p
- a binomial random variable with parameters (n,p)
- a geometric random variable with parameter p
- a Pascal or negative binomial random variable with parameters (r,p)
- a Poisson random variable with parameter (lambda)
- a random variable uniformly distributed on (a,b)
- an exponential random variable with parameter (lambda)
- a gamma random variable with parameters (t, lambda)
- a Gaussian random variable with mean (mu) and variance
(sigma)
^{2} - a bivariate random variable (X,Y) uniformly distributed on a region of the plane

- jointly Gaussian random variables with means (mu)
_{x}and (mu)_{y}respectively, variances (sigma_{x})^{2}and (sigma_{y})^{2}respectively, and correlation coefficient (rho)

A table of values of the unit Gaussian CDF will be supplied to you if it is needed on the exam.

Some of the topics that are on the Powerpoint Slides were not covered in class. Of these, the following will not be on the Final Exam: two functions of two random variables, and more generally, n functions of n random variables except for linear functions; order statistics including min and max, and joint distribution of min and max; conditional pdfs f

_{Y|X}(v|u), the theorem of total probability and Bayes' formula for pdfs; conditional expectation E[Y|X] for continuous random variables; and nonlinear minimum mean-square estimation of Y in terms of X.You are responsible for the following topics: finding the pdf of X-Y, Y/X, X

^{2}+ Y^{2}, sqrt(X^{2}+ Y^{2}); joint pdf of invertible linear transformations of n random variables; circularly symmetric pdfs; jointly Gaussian pdfs; linear minimum mean-square estimation of Y in terms of X; and limit theorems (Lecture 41 of the Powerpoint slides).

**Hour Exams: Combined-section evening hour exams have been scheduled from 7 p.m. to 8 p.m. on Mondays October 9 and November 13.**You may bring one 8.5" by 11" sheet of notes to each hour exam; both sides of the sheet can be used, but the exams are closed-book and closed-notes otherwise. Electronic devices (calculators, cellphones, pagers, laptops, etc.) are neither necessary nor permitted.

You can find copies of old hour exams by going to the web pages of previous offerings of ECE 413.

- a Bernoulli random variable with parameter p