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Philadelphia University
Faculty of Science
Department of Basic Sciences and Mathematics
First Semester, 2015/2016
Course Syllabus
Course Title: mathematical Statistics
Course code: 0250332
Course prerequisite (s) : probability Theory
rd
Course Level: 3
250232
Corequisite (s): --------
Lecture Time: 12:45-:00 (Sun-Tue-Thu)
Credit hours: 3
Academic Staff Specifics
Name
Rank
Office Number
and Location
Office Hours
E-mail Address
10:00-11:00
Dr. Khaled
Assistant
1019 S
(Sun-Tue-Thu)
Alhazaymeh
professor
Faculty of Science
11:30-12:30
khazaymeh@philadelphia.edu.jo
(Mon-Wed)
Prerequisite: Students are expected to have knowledge in probability theory, discrete and continuous
distributions and normal distribution, estimation and tests of statistical hypothesis.
Course module description:
This is an introductory course in mathematical statistics. Topics will include Functions of Random
Variables, Basic Concepts and Examples, The Expected Value and Moments, Random Vectors, Joint and
Marginal Distributions, Independence, Transforms and Sums, Probability Generating Function, Moment
Generating Function, Linear Combination of Normal Random variables, and Point Estimation, Unbiased
Estimators, Method of The Maximum Likelihood.
Course module objectives:
This module aims to:
 Find pdf’s of discrete and continuous random variables,
 Understand and apply the concepts of transformation of random variables,
 Deal with order statistics and find their distributions,
 Learn the methods of moments and maximum likelihood for estimation,
 Understand point and interval estimation for population parameter,
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 Test hypotheses about population parameters,
 Understand the mathematics needed in statistical methods.
Course/ module components
Title: “Introduction to Mathematical Statistics”.
Author(s)/Editor(s): Paul G. Hoel.
Publisher: John Wiley & Sons, Inc.
Edition: 5th Edition.
Year: 1984.
ISBN: 0-13-129382-6.
Teaching methods:
Duration: 16 weeks, 48 hours in total.
Lectures: 48 hours, 3 per week + two exams (two hours).
Assignments: 3 quizzes.
Learning outcomes:

Knowledge and understanding
1. To give the student the necessary information to deals with mathematical statistic problems.
2. To give the student the necessary mathematical statistic tools for further study in pure mathematics.
3. To demonstrate the ability of using mathematical statistic in solving statistic problems.

Cognitive skills (thinking and analysis).
1. To identify and solve problems. Work with given information and handle mathematical statistic
proofs based on mathematical statistic theorems.

Communication skills (personal and academic).
4. Display personal responsibility by working to multiple deadlines in complex activities.
5. Be able to work effectively alone or as a member of a small group working on some tasks.
6. Encourage the students to be self-starters (creativity, decisiveness, initiative) and to finish the
mathematical problems properly (flexibility, adaptability). Also to improve general performance of
students through the interaction with each other in solving different mathematical problems.

Practical and subject specific skills (Transferable Skills).
1. Gaining knowledge and experience of working with many pure mathematical problems.
Assessment instruments
Allocation of Marks
Assessment Instruments
Mark
First examination
20%
Second examination
20%
Final examination
40%
Quizzes, Home works
20%
Total
100%
* Make-up exams will be offered for valid reasons only with consent of the Dean. Make-up exams may
be different from regular exams in content and format.
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Course/module academic calendar
week
(1-4)
Basic and support material to be covered

Functions of random variables:
 Basic concepts, some examples, of discrete and
continuous cases.
 Invertible functions of continuous random variables.
 Expected values for functions of random variables.
 The kth moment of X, variance, the Normal distribution.
(5-8)
First
exam

Random Vectors:
 Basic concepts, definition, joint distributions
 Discrete and continuous distributions.
 Marginal distributions.
 Functions of random vectors.
 Independent random variables.
 Expectation and random vectors.
 Conditional distributions.
(9-12)
Second
exam

Transforms and Sums:
 Notation.
 Probability generating function (p.g . f ).
 Moment generating function (m.g . f .).
 Linear combination of normal random variable.
 The distribution of sample mean.
Homework,
Reports and
their due dates
Quiz 1
Quiz 2
(13-14)

(15)
(16)
Estimation:
 Basic concepts.
 Random samples.
 Statistics.
 Point estimation, unbiased estimators, finding
estimators.
 The method of maximum likelihood.
 Review.

Final Examination.
Expected workload:
On average students need to spend 3 hours of study and preparation for each 50-minute lecture/tutorial.
Attendance policy:
Absence from lectures and/or tutorials shall not exceed 15%. Students who exceed the 15% limit
without a medical or emergency excuse acceptable to and approved by the Dean of the relevant
college/faculty shall not be allowed to take the final examination and shall receive a mark of zero for the
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course. If the excuse is approved by the Dean, the student shall be considered to have withdrawn from
the course.
Module references
Students will be expected to give the same attention to these references as given to the Module textbooks.
Additional Books
1. Malik, S. C., and Savita Arora. Mathematical analysis. New Age International, 1992.
2. Stromberg, Karl R. An introduction to classical real analysis. 1981.