Department of Mathematics, Statistics and Science College of Arts and Sciences Qatar University S T A T 251 C o u r s e S y l l a b u s I n t r o d u c t i o n t o p r o b a b i l i t y A m e e n A l a w n e h, P h. D. A s s o c i a t e P r o f e s s o r o f O p e r a t i o n s R e s e a r c h a n d S t a t i s t i c s E m a i l : a a l a e n e h @ q u. e d u. q a S p r i n g 2 0 0 9 / 2 0 1 0 dr ameen Alawneh Spring 2010
COLLEGE OF ARTS AND SCIENCES DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS STATISTICS PROGRAM Spring 2010 Course Information Course Title: Course Number: Stat 251 Credit Hours: 3 hours: Contact hours: 4 Course Status: Statistics Department Core Curriculum Time: Sun : 8:00 9:50 a.m. Tue Thu, 8:00 9:50, a.m. Location: Sunday : SB 227 Tue Thu : SB 229 Required Text: John Freund s Mathematical Statistics with Applications Miller, I & Mille Pearson -Prentice Hall Inc 2004 7 th Edition Faculty Information Name: Dr Ameen Alawneh Academic Title: Associate Professor Office Location: D 204 Telephone Number: 2164 Email Address: aalawneh@qu.edu.qa Office Hours: Sun: 11:00 12:00 Tue Thu: 9:00 9:50, Math Staff Room A211, Female Building 2
Course Description Random experiment; Events; Counting Techniques; Axioms of Probability; Random Variables; Distribution and Density Functions; Conditional Distributions; Expectation; Moment Generating Functions; Law of Large Numbers and Central Limit Theorem. Course Objectives The course objectives are: 1. To acknowledge students the basic concepts in probability and counting techniques. 2. To understand the fundamental concepts stressed over formal mathematical manipulations 3. To emphasize the use of role of mathematics in finding the moments and then the expectation and variance of a well- known probability distributions discrete and continuous. 4. To gain the probability knowledge needed for further statistics course. 5. To emphasize the usage of probability in practice through solving practical in different disciplines.. Learning Outcomes By the end of this course, students will be able to be: 1. explore and learn about events, sample spaces, probability, compound events, the complement of an event. 2. understand the basic probability concepts, including conditional probability 3. know what is meant by a random variable, and have met the common distributions, with probability mass function and probability density function as appropriate. 4. understand the concepts of expectation and variance of a random variable 5. the ability to extend the idea of the density functions, cumulative, mean and variance to a joint probability distributions 6. compute the conditional expectation and check the independency of random variables. 3
Week Week Starts Content Distribution Course Content Distribution Chapter Title/Topics Material Source Chapter/section in the text 1 21/2 Introduction, review of basic probability rules handout 2 28/2 Combinatorial methods 1.2 3 7/3 Binomial coefficients. Sample space. Events, Probability. Some rules of probability. Conditional probability and 1.3, 2.1-2.7 independent events 4 14/3 Random variables. Probability distributions. Continuous random variables. 5 21/3 Probability density functions. The Multivariate distributions. 3.1, 3.2, 3.3 3.4, 3.5 6 28/3 Marginal distributions. The Conditional distributions 3.6, 3.7 7 4/4 Mathematical expectations: the expected value of a random variable. Moments. Chebyche s theorem. First Exam: Sunday 4/4/2010 4.2, 4.3, 4.4 Spring Break 11/4 15/4/2010 8 18/4 Moment generating functions. Product moments 4.5, 4.6, 9 25/4 Moments of linear combinations of random variables. Conditional expectation 4.7 4.8 10 2/5 Special Probability Distributions: The discrete 5.1 5.4 uniform, Bernoulli, Binomial distributions. 11 9/5 The Negative binomial and geometric. The Poisson. The Multinomial and the Multi Hypergeometric distributions. Second Exam: Thursday 13/5/2010. 12 16/5 Special Probability Distributions: The uniform. The Gamma, exponential and the chi-square. The Beta distribution 13 23/5 The Normal Distribution. The Normal approximation to the binomial 14 30/5 The Bivariate normal distribution 6.7 15-16 Final Exams period June 6, - June 13, 2010 5.7 5.9 6.1-6.4 6.5, 6.6 Laboratory schedule : No Lab Required 4
Delivery Methods We will use different types of teaching methods including: Presentation explaining material. Problem solving. Discussion - actively involving students in learning by asking questions that provoke thinking and verbal response. Cooperative Learning - small group structure emphasizing learning from and with others. Learning Resources & Media 1. Class room meetings with expected participation and discussion. 2. Textbook and references 3. Class material and notes available on the Blackboard. 4. Extensive usage of the Blackboard. calculator and Computer: Each student will need a scientific calculator and access to the internet to complete homework assignments and print off notes and readings Assessment Policy and Tools Assessment Policy and Tools This course will be assessed by exams, assignments, quizzes, active participation during lectures: Assessment Type Day Date Time Weight First Exam Sunday 4/4/2010 8:00 10:00 20% Second Exam Thursday 13/5/2010 8:00 10:00 20% Final Exam TBA TBA TBA 40% Assignments & Participation Multi Motivated and expected TBA 15 minutes Sum 100% 20% 0 5
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 Grades will be final and fair they cannot be negotiated. Although great care is taken in the recording of grades, errors can happen and it is one of your duties to inform me of any discrepancies. A missed homework, quiz or exam counts as a zero. In case of demonstrable illness one of the three exams can be retaken. Description of Exams: Theory: The bulk of questions in the exams will be related to the teory of probability. You should expect proofs and math derivations. Practical: some questions will be on applications from general fields. Learning Activities and Tasks In this course we are using the active engagement student centered environment, where the students are expected to be active during the class. Also Blackboard Academic Suit TM will be used in teaching and learning. Course Regulations Student Responsibilities and Attendance Policies and Procedures 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. Students are expected to be punctual (every 3 late class arrivals will be counted as 1 class absence) in class attendance and to conduct themselves in an adult and professional manner. 6
Homework assignments and library assignment should be worked independently. Exchanging ideas are permitted orally but don't require any kind of copying. Homework assignment should be submitted in organized way and any late assignments may be assessed and corrected but the grade will be zero. Plagiarism (Academic Dishonesty) 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. Using part of, or the entire work, prepared by another or turning in a homework assignment prepared by another student or party are examples of plagiarism. 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. 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 behaviours 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. Plagiarism includes the following examples and it applies to all student assignments or submitted work: Use of the work, ideas, images or words of someone else without his/her permission. Use of someone else's wording, name, phrase, sentence, paragraph or essay without using quotation marks. Misrepresentation of the sources that were used. For further information see: http://www.plagiarism.org/ 7
The instructor has the right to fail the coursework or deduct marks where plagiarism is detected Classroom Discipline The use of mobile telephones inside the classroom is NOT allowed. Any student disciplinary issues, which may arise, will be referred to the head of the Department. Additional Sources Printed Sources -The references are available in the Qatar University library 1) A first course in probability by Chandra, T. K., Boca Raton CRC Press, 2001. 2) Miller & Freund's Probability and statistics for engineers, by Richard A. Johnson, Prentice Hall International (London), 6 th edition, 2000. -A student may make his own class notes. Some material related to the class will be available on the blackboard Non-Printed Sources.Group discussions in the class. Online Sources You may find too many examples, extensive discussion in the website, e.g. http://www.astrohandbook.com/ch17/intro_probability.pdf 8
Appendices Course Objectives 1. To acknowledge students the basic concepts in probability and counting techniques. Matrix of Objectives and Outcomes Course Learning Outcomes Explore and learn about events, sample spaces, probability, compound events, the complement of an event. Understand the basic probability concepts, including conditional probability Introduction to probability Assessment tools Exams Assignments 2. To understand the fundamental concepts stressed over formal mathematical manipulations 3. To emphasize the use of role of mathematics in finding the moments and then the expectation and variance of a well- known probability distributions discrete and continuous. 4. To gain the probability knowledge needed for further statistics course. 5. To emphasize the usage of probability in practice through solving practical in different disciplines. Know what is meant by a random variable, and have met the common distributions, with probability mass function and probability density function as appropriate. Understand the concepts of expectation and variance of a random variable The ability to extend the idea of the density functions, cumulative, mean and variance to a joint probability distributions Compute the conditional expectation and check the independency of random variables. Know what is meant by a random variable, and have met the common distributions, with probability mass function and probability density function as appropriate Exams Assignments Exams Assignments Exams Assignments Exams Assignments dr ameen Alawneh Spring 2010
Assignments Rubrics Instructor name: Dr Ameen Alawneh Student Name: CATEGORY 4 3 2 1 Organization Information is very organized with well-constructed paragraphs and subheadings. Information is organized with well-constructed paragraphs. Information is organized, but paragraphs are not well-constructed. The information appears to be disorganized. 8) Amount of Information All topics are addressed and all questions answered with at least 2 sentences about each. All topics are addressed and most questions answered with at least 2 sentences about each. All topics are addressed, and most questions answered with 1 sentence about each. One or more topics were not addressed. Quality of Information Information clearly relates to the main topic. It includes several supporting details and/or examples. 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. Sources All sources (information and graphics) are accurately documented in the desired format.references clearly stated. All sources (information and graphics) are accurately documented, but a few are not in the desired format. Refernces clearly stated All sources (information and graphics) are accurately documented, but many are not in the desired format. Not all refernces are included Some sources are not accurately documented or there are no references included. 10
Mechanics No grammatical, spelling or punctuation errors. Almost no grammatical, spelling or punctuation errors A few grammatical spelling, or punctuation errors. Many grammatical, spelling, or punctuation errors. Diagrams & Illustrations Diagrams and illustrations are neat, accurate and add to the reader's understanding of the topic. Diagrams and illustrations are accurate and add to the reader's understanding of the topic. Diagrams and illustrations are neat and accurate and sometimes add to the reader's understanding of the topic. Diagrams and illustrations are not accurate OR do not add to the reader's understanding of the topic. Paragraph Construction All paragraphs include introductory sentence, explanations or details, and concluding sentence. Most paragraphs include introductory sentence, explanations or details, and concluding sentence. Paragraphs included related information but were typically not constructed well. Paragraphing structure was not clear and sentences were not typically related within the paragraphs. 11