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-testfor 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).