Department of Mathematics, Statistics and Science College of Arts ...

STAT 211

INTRODUCTION TO PROBABILITY

Department of Mathematics, Statistics and Science College of Arts and Sciences Qatar University

STAT 211 INTRODUCTION TO PROBABILITY

AMEEN ALAWNEH, PH.D. ASSOCIATE PROFESSOR OF STATISTICS AND OPERATIONS RESEARCH EMAIL: [email protected]

FALL 2012

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STAT 211


Course Information Course Title Course Number Credit Hours: Prerequisites

Introduction to Probability STAT 211 3 hours

Group L51 Contact hours

STAT 101 and MATH 102 Day(s) Time Class time and location Sun - Tue 10:00 – 11:50 Semester Fall 2012 Semester Start Date September, 16th , 2012 Last day of classes Thursday 27/12/2012 Final Exam Period 30/12/2012 – 10/1/2013 Qatar National Day Sunday 18/12/2012 Number of weeks 15 weeks

4 hours Room Room: A212

Text Book & References Title Authors

Introduction to Probability G. Roussas

Book Image Publisher Edition/Year

References

Academic Press First, 2007 1John E. Freund's Mathematical Statistics. Miller & Miller, 7th Edition, 2003, Prentice Hall. 2Probability and Mathematical Inference. Hogg and Tanis, 8th Edition, 2009, Prentice Hall. 3Introduction to Mathematical Statistics. Hogg, Craig and McKean, 6th Edition, 2004, Prentice Hall.

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Faculty Information Instructor Department Program Office Location Office phone Office Hours E-mail

Dr Ameen Associate Professor STAT 211 Alawneh, INTRODUCTION TO PROBABILITY Mathematics, Statistics and Physics Statistics B212 Corridor 2 Science Male Building 4628 Sun -Tue: 12:00 -12:50 Mon - Wed: 11:00 – 11:50 Or by appointment [email protected]

Math staff room/Science Building Room A210

Course Description and Contents STAT 211 “Introduction to Probability” is a three credit hours course. It is a compulsory course for the students in the Statistics program. STAT 211 is a core course used to build a strong theoretical background that enable students to deep understanding of the Statistical concepts and techniques in the other courses. The content of the course includes Random experiment. Sample spaces, Events. Axioms and rules of probability. Equally likely sample spaces. Counting techniques, Conditional probability. Random variables. Expected values. Moment generating function. Probability generating function, Probability distributions, uniform, Bernoulli, binomial, geometric, negative binomial, Poisson and hypergeometric. exponential, gamma, beta and normal. Discrete and continuous bivariate random variables. Joint, Marginal and conditional distributions.

Course Objectives 1) Familiarizing the student with the foundations of probability and the basic probability tools and methods. 2) Acquainting students with random variables and probability distributions. 3) Acquainting students with some discrete and continuous probability models. 4) Introducing some probability theorems and their useful applications. 5) Familiarizing students with some multidimensional random variables 6) Familiarizing students with some mathematical tools needed in statistics.

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STAT 211


Student Learning Outcomes(SLOs): Upon completion of this course, the student will be able to: 1) Calculate probabilities and other relevant quantities from probability distributions 2) Select the suitable probability distributions for certain problems 3) Derive the expectations, moment generating functions and the cumulative distribution functions for certain probability distributions 4) Use inequalities and certain theorems to establish certain useful properties of probability distributions. 5) Work with certain multivariate distributions and derive marginal and conditional probability distributions

Course Content Distribution Week

Week Start date

1

16/9

Some Fundamental Concepts: Some fundamental results, Random variables

2

23/9

Basic concepts and results in counting

3

30/9

The concept of probability and basic results: Definition of probability. Some basic properties results

4

7/10

Distribution of random variables. Quiz 1

3.3

5

14/10

Conditional probability and independence: Conditional probability and related results.

4.1

Sunday: Review and Problem Solving Tuesday 23/10/2012 “ First Exam” Eid Aladha Independent Events and Related results.

4.2

6

21/10 28/10

4/11

7 8

11/11

9 10

18/11 25/11

11 12 13

2/12 9/12 16/12

14 15

23/12

Chapter Title/Topics

Numerical Characteristics of a random variable: Expectation, variance and Moment. Quiz 2 Generating function of a random variable Some special distributions Some special discrete distributions. Quiz 3

Some special continuous distributions Sunday: Problem solving. Tuesday: Second Exam Joint probability density function of two random variables and related inequalities: Joint d.f. and joint joint p.d.f. of two random variables. Quiz 4 Marginal and conditional p.d.f’s, conditional expectation and variance

Final Exams: Wednesday 8/1/2013

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Material Source Chapter/section 2.1, 2.2

2.3 3.1, 3.2

5.1 5.2 6.1 6.2

7.1 7.2

STAT 211


Matrix of Objectives and Outcomes

Course Objectives Familiarizing the student with the foundations of probability and the basic probability tools and methods.

Course Learning Outcomes Calculate probabilities and other relevant quantities from probability distributions

Acquainting students with random Calculate probabilities and other relevant quantities variables and probability distribu- from probability distributions. Select the suitable probability distributions for certain tions. problems Acquainting students with some discrete and continuous probabil- Select the suitable probability distributions for certain problems. ity models. Derive the expectations, moment generating functions and the cumulative distribution functions for certain probability distributions. Introducing some probability theorems and their useful applications

Use inequalities and certain theorems to establish certain useful properties of probability distributions.

Familiarizing students with some Work with certain multivariate distributions and demultidimensional random variarive marginal and conditional probability distributions bles. Familiarizing students with some mathematical tools needed in statistics.

Derive the expectations, moment generating functions and the cumulative distribution functions for certain probability distributions. Work with multivariate distributions and derive marginal and conditional probability distributions

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Assessment tools Exams Quizzes Assignments Exams Quizzes Assignments

Exams Quizzes Assignments

Exams Quizzes Assignments Exams Quizzes Assignments

Exams Quizzes Assignments

STAT 211

INTRODUCTION TO PROBABILTY

.Assessment Policy and Tools This course will be assessed by exams, assignments and quizzes as follows:

Assessment Type First Exam Second Exam Final Exam Assignments Quizzes Participation Sum

Day Date Time Tuesday 23/10/2012 10:00 – 11:30 Tuesday 11/12/2012 10:00 – 11:30 Wednesday 8/1/2012 08: - 10:00 Multi Check content distribution Expected

Weight 20% 25% 35% 10% 10% 0 100%

For more details about exams, lectures, rules, etc. http://www.qu.edu.qa/ar/students/registration/registrer/final_exams.php

Assessment Policy: Grades for the course will be assigned as follows: A

B+

B

C+

C

D+

D

F

90-100

85-89.9

85-89

75-79.9

70-74.9

64-69.9

60-64.9

59.9-0

Methods of Teaching 1) Class room presentations on regular basis. 2) Using Statistical packages –Minitab - to apply the all statistical concepts especially for huge data. 3) Problem solving. 4) Discussion - actively involving students in learning by asking questions that provoke thinking and verbal response 5) Cooperative Learning - small group structure emphasizing learning from and with others.

STUDENT WITH DISABILITIES

If you have a special needs because of psychological or medical disabilities you can contact me to make an appropriate arrangement according to QU regulations.

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 Theory: The main part of exams will be theory and derivations. Exams Descrip- tion  Practical: Only some questions will be detected to practical problems.  All exams are closed book and notes Exams  Cheating is prohibited. Regulations  Expect different types of questions: multiple choice, True or False and problem solving. Final exam The final exam is comprehensive. Incomplete exams need excuse (illness or any other unfortunate conseIncomplete exams quence, certified). Students Presentation No formal presentations are expected from the student Quizzes 3 – 4 quizzes, Students will be required to work either independently, or in groups, to In-Class Assignments complete assignments during class time. These assignments are to make sure they understand the main concepts before we proceed. First and second: in the regular class time and room Exams Date and Time

Cheating Cell Phones

Final: 8/1/2013 Prohibited; and in case of cheating the student will be subject to punishment according to QU regulations. The instructor has the right to fail the coursework or deduct marks where plagiarism is detected Keep them out of sight and turned off. No cell phones during exams.  Assignments should be worked independently. Exchanging ideas are permitted orally but don't require any kind of copying.

Assignments

 Assignment should be submitted in organized way and any late assignments may be assessed and corrected but the grade will be zero.

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Attendance AND Withdrawal

Attendance

Class attendance is compulsory. In accordance with University regulations, a student’s absence cannot exceed 25% of the total number (entire semester) of class meetings. If your absence rate exceeds 25%, including both excused and unexcused absences, you will NOT be allowed to take the final examination and will receive an ‘F barred’ grade for the course.

Late Arrival

Students are expected to be punctual (every 3 late class arrivals will be counted as 1 class absence) in class attendance.

Withdrawal

The last day to withdraw a course with a grade “W” is Thursday 15/11/2012.

Learning Resources & Media  Class room meetings with expected participation and discussion.  Textbook: The textbook is the main source of the material presented in the class. So, it is required to have a copy of the textbook.  References: The references are available at Qatar university library. You can use the reference for extra examples or application.  Assignments: I will assign two types of problems. Some to hand in by exact due date and others for further practice and discussion.  Quizzes: In case we want to make quizzes I will determine the material and the time in advance.  Extensive usage of blackboard to present some class material- class notes, assignments, syllabus, assignments and exams solutions, etc.  Office hours: -Four hours in the math staff room female campus or by appointment.

On-Line Recourses 1) The Probability web, http://www.statslab.cam.ac.uk/probweb/ 2) Math forum internet library, http://mathforum.org/library/view/2543.html 3) Mathematical resources in the web, http://www.math.ufl.edu/math/math-web/mathmost.html

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Learning Activities and Tasks  Education aimed to develop cooperation among students  Good learning is collaborative and social rather than competitive and isolated  Always try to talk and write about what you learn and relate it to your past experience and apply it in your daily life.  we are using active learning engagement centered where students are expected to be active during the class .  Blackboard Academic Suit TM will be used in teaching and learning.  Mathematically speaking Time + Energy = Effective Learning Effective Learning → Successful Study coaching in this course is accomplished through the following: Class meetings Feel free to ask any question related to the material presented in the ( lectures) class during the class time. I encourage you to ask or discuss any ambiguity in the ideas or exerOffice hours cises in the predetermined office hours or by appointment or via the blackboard or email. The listed references and/or any elementary Statistics book availaReferences: ble in the library are helpful.

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IINTRODUCTION TO PROBABILTY

Plagiarism (Academic Dishonesty) “Plagiarism is considered a serious academic offence and can result in your work losing marks or being failed. QU expects its students to adopt and abide by the highest standards of conduct in their interaction with their professors, peers, and the wider University community. As such, a student is expected not to engage in behaviors that compromise his/her own integrity as well as that of QU. You may discuss assignments and projects with each other, but you should do the work yourself. In the case of group projects, you will be expected to do your share of the work. If you use someone else's words or ideas, you must cite your sources. Any student disciplinary issues, which may arise, will be referred to the head of the Department”. Plagiarism includes the following examples and it applies to all student assignments or submitted work: 1) Using part or the entire work, ideas, images or words of someone else without his/her permission. 2) Use of someone else's wording, name, phrase, sentence, paragraph or essay without using quotation marks. 3) Misrepresentation of the sources that were used. 4) Using part of, or the entire work, prepared by another or turning in a homework assignment prepared by another student or party Related Important Notes 1) All students are expected to turn in work that is their own. Any attempt to pass off another's work as your own will constitute an "F" in the entire course 2) The instructor has the right to fail the coursework or deduct marks where plagiarism is detected 3) You may discuss assignments and projects with each other, but you should do the work yourself. In the case of group projects, you will be expected to do your share of the work. If you use someone else's words or ideas, you must cite your sources.

For further information see: http://www.plagiarism.org/

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IINTRODUCTION TO PROBABILTY

. Assignment Rubrics* Student name:……………………………

Category

Organization

Amount of Information

Quality of Information

Sources

4 Information is very organized with well-constructed paragraphs and subheadings. All topics are addressed and all questions answered with at least 2 sentences about each. Information clearly relates to the main topic. It includes several supporting details and/or examples. All sources (information and graphics) are accurately documented in the desired format. References clearly stated.

Instructor name: Dr Ameen Alawneh

3

2

1

Information is organized with well-constructed paragraphs.

Information is organized, but paragraphs are not wellconstructed.

The information appears to be disorganized. 8)

All topics are addressed and most questions answered with at least two sentences about each.

All topics are addressed, and most questions answered with one sentence about each.

One or more topics were not addressed.

Information clearly relates to the main topic. It provides 1-2 supporting details and/or examples.

Information clearly relates to the main topic. No details and/or examples are given.

Information has little or nothing to do with the main topic.

All sources (information and graphics) are accurately documented, but a few are not in the desired format. References clearly stated

All sources (information and graphics) are accurately documented, but many are not in the desired format. Not all references are included

Some sources are not accurately documented or there are no references included.

Total

*This rubric has been published by college of Arts and Science/Qatar University.

11

Score