ECE 313 Late-Breaking News

- You are allowed to bring TWO 8.5" by 11" sheets of notes to the exam;
both sides of the sheets can be used.
Calculators, laptop computers, Palm Pilots and the like are not 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 negative binomial random variable with parameters (n,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.

You may use the expressions for the means and variances of these random variables in computing numerical values on the exam. For example, if I describe a situation in which a certain measurement can be modeled as a binomial random variable, and ask for E[X], you need not explicitly show all the details of how you computed the sum of u

_{i}p_{X}(u_{i}). I will accept an answer of the form:- Since X is a binomial random variable with parameters (100, 0.3), E[X] = 100*0.3 = 30.

- E[X] = 30

### The Final Examination is comprehensive in that much of the subject matter covered in the entire course is included on the exam. However, there is considerably more emphasis on the material not covered on the two Hour Exams, and the material covered after the Second Hour Exam. It is recommended that you pay particular attention to topics such as

- univariate CDFs, pdfs and pmfs
- computation of the probability that X lies in an interval
- mean, variance, and LOTUS
- computation of the pdf/pmf of a function of one random variable
- the Poisson random process
- conditional pmfs and pdfs
- joint pdfs and pmfs
- computation of marginal pdfs and pmfs
- computation of the probability that (X,Y) lies in a region of
the plane
- computation of the pdf/pmf of ONE function of two random variables
- covariance, correlation coefficient, variance of a sum of random
variables, covariance of aX+bY and cX+dY, etc.
- jointly Gaussian random variables
- minimum-mean-square-error and linear minimum-mean-square-error
estimation of one random variable in terms of another

As to what is not included on the Final Exam, there will be no questions on

- Decision theory, maximum-likelihood decision rules, Bayesian decision
rules, etc.
- Characteristic functions
- joint pdf of two or more functions of two or more random variables
except that the joint distribution
of the maximum and minimum of two variables, and of linear transformations
of jointly Gaussian random variables are part of the material on
which I might ask a question

- a Bernoulli random variable with parameter p