ROWAN
UNIVERSITY

Department
of Mathematics

Syllabus

**Math 01.517
Engineering Probability and Statistics
**

**Course Description:**

** **

**Math 01.517 Engineering Probability and Statistics 3 s.h.**

Students in
this course will be introduced to various mathematical and statistical models
and techniques for analyzing data. This will include summarizing data; using
probability distributions to model processes; using interval estimation for
population parameters based o sample data; designing and performing tests about
population parameters based on sample data; identifying and applying regression
models that describe the relationship between a dependent variable and one or
more independent variables.

**Objectives:**

Students in this course will become familiar with various
mathematical models and statistical techniques of analyzing data.

At the end of this course, students will be able to:

- summarize and present data using numerical
measures and graphical techniques,
- use the different probability distributions of
random variables to model processes,
- use interval estimation for population parameter
(s) based on sample data,
- design and make tests of hypothesis about
population parameter (s) based on sample data, and
- identify regression models that describe the
relationship between a dependent variable and one or more independent
variables.

**Topical Outline:**

Topics that may be covered include.

- Introduction to probability: Axiomatic
definition, conditional and joint probabilities, Bayes' theorem and
applications, combinatorics
- Random variables: Probability density functions,
some special discrete and continuous random variables, expected value of a
random variable, moment generating functions.
- Vector valued random variables: Joint
distributions and densities, covariance matrices and transformations.
- Descriptive statistics: Random sampling,
measures of location and variability of data, graphical representation of
data.
- Estimation and Hypothesis Testing: Sampling
Distributions, the Central Limit Theorem, interval estimation, parametric
and nonparametric tests in making inferences.
- Regression models: Correlation, description of
the model, linear, polynomial and multiple regression.
- Some applications: estimation of failure rates,
failure time distribution models, quality control calculations.

**Texts:**

The following books may be used as
texts for the course.

I.
Devore, Jay (1982) Probability and Statistics for
Engineering and the Sciences, Brooks/Cole.

II.
Milton, J. S. and Arnold, J. C., (1995), Introduction to
Probability and Statistics: Principles and Applications for Engineering,
McGraw-Hill.

III.
Kennedy, J. B., and Neville, A. M., (1986), Basic
Statistical Methods for Engineers and Scientists, 3^{rd} edition,
Harper and Row.

IV.
Miller, I. R., Freund, J. E., and Johnson, R., (1990),
Probability and Statistics for Engineers, 4^{th} edition,
Prentice-Hall.