Instructions for the Final Exam

The final exam will be given in two parts. The first part (which will count as 80% of the total
score on the final exam) will be given in class on Monday, November 27 between 12:30  and 2:30.
The second part (20%) will be take-home and it will cover material from the programming
language Maple. No collaboration is allowed on either part of the exam. Cheating will be penalized
by at best giving a lower letter for the course grade.

For the in-class part of the exam you are allowed with 2 sheets of paper (4 pages) of formulas
from the course, in addition to the tables for the normal, t-distribution, chi-square, and F distributions.
Also,  you may use calculators, but you have to show your work for every step in your solution
(including integration, substitution, use of identitites, etc.).

A comprehensive list of subjects on which you may be tested:

Statistics
--
Averages, Variance, Covariance, Correlation coefficient for random variables
-- T- distribution - definition, the  100 * u percentile of a t-distribution
-- Confidence interval for the mean of a normal distribution (computing the sem = standard
error of the mean by using the sample standard deviation).
-- Chi-square distribution - definition, the 100 * u percentile of a chi-square distribution
-- Confidence interval for the variance of a distribution
-- Hypothesis Testing ; definition of H_0 and H_1; One tailed test for the mean of a normal
distribution (p-values and their significance).
-- Linear Regression; Total SS, Reg SS, Res SS. The F distribution. The F-test for simple
linear. The t-test for simple linear regression. The p-value of the test. CIs for the regression
parameters. Relationship between the Pearson correlation coefficient and the regression
parameter b.
-- Multiple Regression. The F-test for assessing if some variables are good predictors for
the dependent variable ; the p-value of the test. The t-test (or the F-test) for assessing if
one variable is significant when all the other variables are significant in predicting the
dependent variable; the p-value(s) of the test.
-- Multiple Logistic Regression. The logit transformation. The odds ratio OR and its
interpretation.
-- Rank correlation. Ranking procedure. The Spearman rank-correlation coefficient and
the t-test
for Spearman rank correlation (the p-value of the test).

Traffic Models

-- Definition of velocity, density, flow for the continuum model of traffic flow
-- Flow=density * velocity
-- the conservation law of traffic; interpretation of terms and derivation
-- relationship between density and velocity; Fundamental Diagram of Traffic flow
Light and heavy traffic
-- solving linear conservation laws; ICs and BCs; characteristics
-- linearization of nonlinear conservation laws

Matrix Theory
--
Solving a linear system of equations with row reduction
--  Linear dependence and independence
-- Linear transformations. The matrix of a linear transformation
--  Finding eigenvectors and eigenvalues. Generalized eigenvectors (the case of
duplication for eigenvalues)

Maple
--
define functions, plot graphs
-- solve ordinary and partial differential equations, plot solution curves and solution surfaces
--
compute eigenvectors and eigenvalues
-- plot curves and surfaces in the same system of coordinates; plot a sequence of ``points" (i.e. disks)
or curves in the same system of coordinates (for ... from ... do...od; procedure).