Probability Distribution Theory   نظرية التوزيعات الإحتمالية

Course Code	Stat 202	رقم المقرر ورمزه
Credit Hours	3	الوحدات الدراسية
Level	3rd Level الثالث	المستوى
Prerequisite	Stat 101 + Math 202	المتطلب السابق

وصف محتويات المقرر :                                                 : Course Contents

Introduction and overview of Definition of the probability,  Definition of the random variable – the probability function of the  discrete   random variable  - the density probability function of the continuous random variable, The Expectation and the variance of the random variable (Discrete and Continuous), Discrete probability Distributions (Bernoulli, Binomial and Poisson), Continuous probability distribution (Normal distribution and its application). -  Approximate probabilities for some binomial and Poisson distributions, Other probability distributions: uniform, exponential, and gamma distributions, functions of random variables- mathematical expectation- the moment generating function, Properties of mathematical expectation.

التوزيعات الاحتمالية المنفصلة (دالة الكتلة الاحتمالية وخواصها - التوقع الرياضي والتباين والانحراف المعياري والدوال المولدة للعزوم للتوزيعات المنفصلة).التوزيعات الاحتمالية المتصلة (دالة الكثافة الاحتمالية وخواصها - التوقع الرياضي والتباين والانحراف المعياري والدوال المولدة للعزوم للتوزيعات المتصلة).المتغيرات العشوائية الثنائية المنفصلة والمتصلة و خواصها (التوقع للمتغير العشوائي الثنائي، التباين المشترك (التغاير)، معامل الارتباط للمتغير العشوائي الثنائي، التباين لمجموع أو الفرق بين متغيرين ، الدوال المولدة للعزوم للمتغير العشوائي الثنائي).التوزيعات ذات المتغيرين (التوزيعات الهامشية والشرطية - استقلال متغيرات عشوائية- التوقع الشرطي).توزيعات دوال في متغيرات عشوائية.العينات العشوائية (توزيع متوسط العينة – قانون الأعداد الكبيرة – نظرية النهاية المركزية).

Course components (total contact hours and credits per semester):
Credit		Contact     Hours				Self-Study	Other	Total
ECTS	NCAAA	Lecture	Tutorial	Laboratory	Practical
5 cp	3 ch	30	15	0	0	78	11	134 ch

·Follow on from, and reinforce, a level mathematics.

·Present students with a wide range of mathematics ideas in preparation for more demanding material later.

· Enable students to apply Mathematical tools/ techniques to product project Broaden skills in team work, critical thinking, communication, planning and scheduling through design project

· Enable students to consider safety, ethical, legal, and other societal constraints in execution of their design projects

Outcomes:

1. Know how a team can use the Statistical Inference process to carry out a project

2. Solve open-ended problems, cope with decision making and satisfy competing objectives

3. Apply knowledge, as needed, to design a satisfactory system to achieve a final successful project

4. Prepare a needs-assessment and define a deliverable for a project

5. Understand the impact of aesthetic and human aspects

6. Use and integrate the fundamentals studied previously towards the goal of analyzing and designing project to achieve

7. Deliver a final oral presentation for their project.

8. Produce final design report as part of their deliverable

9. Use appropriate software for project, modeling, and analysis

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List of Topic	No. of Weeks	Contact hours
		Lecture	tutorials
Introduction and overview of Definition of the probability- Definition of the random variable – the probability function of the discrete random variable - the density probability function of the continuous random variable	2	6	2
The Expectation and the variance of the random variable (Discrete and Continuous)	3	9	3
Mid-term 1		1
Discrete probability Distributions (Bernoulli, Binomial and Poisson)	3	9	3
Continuous probability distribution (Normal distribution and its application). - Approximate probabilities for some binomial and Poisson distributions.	2	6	2
Mid-term 2		1
Other probability distributions: uniform , exponential , and gamma distributions .	3	9	3
- functions of random variables- mathematical expectation- the moment generating function. . Sampling distributions	2	6	2
Mid-term 3		1
Final Exam		2
Total

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References:

الكتب المقررة والمراجع :

1. Perm S. Mann: Introductory Statistics, John Wiley and sons, Inc., 2001

2. Harry Frank, Steven C. Althoen: Statistics concepts and Applications. Cambridge University Press, 1994.

3. جلال الصياد: نظرية الاحتمالات ، دار حافظ للنشر والتوزيع ،السعودية ،(الطبعة الرابعة) 1421 هـ / 2000م.

4.  Applied Statistics and Probability for Engineers. Seventh edition D.C. Montgomery & G. C. Runger John Wiley & Sons. 2011: 13:978 -0-470-05304-1

5.  A Modern Introduction to Probability and Statistics Frederik MIChel Dekking Cornelis Kraaikamp Hendrik Paul Lopuhaa ¨Ludolf Erwin Meester Springer-Verlag London Limited : 2005: 13: 978-1-85233-891-1

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المحاضرات

Download		Lecture Name
PDF	PPT	Set Theory
PDF	PPT	Applying set theory to probability
PDF	PPT	Independence
PDF	PPT	Tree Diagram
PDF	PPT	Counting Techniques
PDF	PPT	Discrete Random Variable
PDF	PPT	Cumulative Distribution function
PDF	PPT	(Averages (Expected Value
PDF	PPT	Function of Random Variable
PDF	PPT	2 Function of Random Variable
PDF	PPT	Variance and standard Deviation
PDF	PPT	Continuous Random Variables
PDF	PPT	Some Useful Continuous Random Variables

Tests  نماذج إختبارات
Semester الفصل الدراسي	Academic Year العام الدراسي	Download تحميل
Final 1st الأول	1432	PDF
Mid-term Exam اختبار فصلي	1433	Docx
Final 2nd الثاني	1433	PDF
Final 2nd الثاني	1435	PDF

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Questions Bank Probability Distribution Theory Stat 202

Questions Bank- STA 101

Questions Bank-STA 224

Questions Bank- STAT 212

Questions Bank- STAT 202

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Videos related to the course فيديوهات  دراسية متعلقة بالمقرر

Introductory Statistics : Probability distributions

Discrete Random Variables

Expected Value: E(X)

Probability Density Functions / Continuous Random Variables

Standard Normal Distribution

Normal Distribution & Z-scores