Department of Electrical and Computer Engineering

ECE 313 Late-Breaking News


The Final Examination is scheduled for Friday December 14, 2001 from 8:00 a.m. to 11:00 a.m. in Room 260 Everitt Laboratory.

  • 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
    and
    • jointly Gaussian random variables with means (mu)x and (mu)y respectively, variances (sigmax)2 and (sigmay)2 respectively, and correlation coefficient (rho)

    If you have forgotten the formulas for the pmf/pdf/CDF or the mean and variance of these (or do not have them written down on your sheets of notes,) you will not be given these pieces of information during the exam.

    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 uipX(ui). 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.

    I will not accept the bald and unadorned statement

    • E[X] = 30

    with no explanation whatsoever. In short, I am looking for a statement that shows that you have recognized from the word description that X is a binomial random variable, and what its parameters are.


    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

    I have not yet decided whether to include multiple-choice or TRUE/FALSE questions on the Final Exam.

    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