Name of module: Statistical Methods in EngineeringNumber of module: 362-1-3061

Module description:

A standard probability and statistics course.

Aims of the module:

Expose the student to basic notions from probability and statistics, their usageand meaning through various example problems in science and engineering.

Objective of the module:

To get the student acquainted with the basic method of probability. We begin withan introduction to the concept of probability and its various interpretations. Its mathematical foundations are demonstrated in some seemingly counter-intuitive examples. We go through the axiomatic definition of probability space to the useful concept of a random variable. From that points onward we focus on the statisticsof random variables, including distributions, density functions and joint statistics. We also touch upon statistical inequalities, the law of large numbers and the centrallimit theorem. The Monte-Carlo method is introduced and analyzed through examples.

Learning outcomes of the module:

1. Translate a problem into the language of probability.2. Use the axioms to answer probabilistic questions.3. Use random variables effectively to tackle probabilistic problems.4. Comprehend with the concept of probability distribution and density function.5. Use statistical methods for estimating unknown and uncertain quantities.

Attendance regulation: None.

Teaching arrangement and method of instruction: There are 3 lecture hours and 2 tutorialper week. There are total of 13 lectures. There are optional homework assignment on thecourse website in Moodle.

Assessment:

The final mark is composed of the following components:

1. Midterm work which will form 40% of the final grade (Magen).2. Final exam which will form 60% of the final grade.

Work and assignment:

There is a midterm work (40% Magen) and optional homework assignments on the coursewebsite in Moodle.

Time requirement for individual work: no such requirement.

Module content\Schedule outline:

The following topics are covered.

1. Axioms of probability: introduction to set theory, set operations, probability space, conditional probability, total probability, Bayes theorem, statistical independence. (4 hr)

2. Repeated trials: combined experiments, independent experiments, Bernoulli trials. (4 hr)

3. Random variables: introduction to the concept of a random variable, distribution anddensity function, continuous, discrete and mixed random variables. (4 hr)

4. Example distributions, conditional distributions. Function of one random variable. (4 hr)

5. Statistics of random variables: mean and variance. Inequalities: Tchebysheff and Markov. (4 hr)

6. Two random variables: joint statistics and examples. (3 hr)

7. Series of random variables: convergence theorems, law of large numbers, centrallimit theorem. (4 hr)

8. Monte-Carlo integration. (3 hr)

9. Statistical estimation methods. Least squares, Maximum likelihood, Hypothesis testing. (5 hr)

10. Stochastic systems, random processes, basic filtering. (4 hr)

Required reading: None.

Additional literature:

A. Papoulis, “Probability, Random Variables, and Stochastic Processes.” (3rd edition onward), McGraw-Hill

Ben-Gurion university of the NegevMechanical Engineering

BGU credit: 3 pts

ECTS credit: do not know.

Academic year: 2014-2015

Semester: Fall

Hours of instructions: 3 lecturehours per week, 2 tutorial hours per week.

Location of instruction: Marcuscampus BGU.

Language of instruction: Hebrew

Cycle: first.

Position: Obligatory.

Field of education: Mechanicalengineering.

General prerequisites:Algebra, Calculus.

Grading scale: 0 - 100 (0 lowest). Passing gradeis 56.

Lecturer: Dr. Avishy Carmi.

Contact details: Room 312,Building #55.Phone: 08-6477084.Email:

Office hours: Thursday, 12:00 to 14:00.

avcarmi@bgu.ac.il

Module evaluation:

Regular BGU evluation process.At the end of the semester thestudents will evaluate themodule, in order to draw conclusions, and for theuniversity internal needs.

Last update: 2 Dec 2014