Mathematical Statistics I
๐ Mathematical Statistics I
Rigorous mathematical treatment of statistical theory tailored for Economics and Finance students, covering probability foundations, random variables, and distribution theory with applications to economic and financial data analysis.
๐ Quick Navigation
๐ Course Topics
Unit 1: Combinatorial Foundations
Unit 2: Probability Theory
Unit 3: Discrete Random Variables
Unit 4: Continuous Random Variables
Unit 5: Multivariate Distributions
๐ Course Information
๐ฏ Learning Objectives & Program Alignment
Collect and assess required economics data by applying appropriate statistical methodology and use of statistics software
Contributes to PLO 2: Acquire and organize information relevant to economics using various resources and digital technologiesInterpret the results of probability calculations, statistical measures, and distribution analyses to draw objective conclusions about economic and business-related phenomena
Contributes to PLO 4: Interpret the results of empirical and theoretical analyses to draw objective conclusionsIdentify, analyze, and solve problems involving combinatorial analysis, probability theory, and random variables by applying theoretical concepts and empirical methods
Contributes to PLO 5: Identify, analyze, and solve problems by applying theoretical knowledge and empirical toolsDevelop innovative solutions to economic problems by applying probability theory, distributions, and statistical analysis through detailed examination
Contributes to PLO 6: Develop innovative solutions to economic problems through in-depth analysis๐ Course Topics & Interactive Lectures
Unit 1: Combinatorial Foundations
Topic 1: Basic Counting Principles
๐ฅ Combinatorial Analysis.
Business Related Explanation of Combinatorial Analysis
Unit 2: Axioms of Probability
Topic 2: Introduction To Probability. Sample Spaces and Events
๐ฅ Axioms of Probability. Introduction.
Simple xplanation of probability axioms and birthday paradox.
Topic 3: Sample Spaces with Equally Likely Outcomes
๐ฅ Sample Spaces With Equally Likely Outcomes.
Equally Likely Outcomes. Business Related Explanation.
Unit 3: Conditional Probability & Independence
Topic 4: Conditional Probability
๐ฅ Conditional Probability
Conditional Probability and some applications in Economics and Finance.
Topic 5: Independence of Events
๐ฅ Independence of Events
Comprehensive explanation of event independence and its practical applications in economics and finance.
Topic 6: Bayes Theorem & Economic Applications
๐ฅ Bayes Theorem
Bayes' theorem and its practical applications in economics and finance.
Unit 4: Discrete Random Variables
Topic 7: Discrete Probability Distributions
๐ฅ Discrete Probability Distributions
Introduction to discrete random variables and probability distributions with business applications.
Topic 8: Binomial Distribution
๐ฅ Binomial Distribution
Investment success rates and market penetration modeling with binomial distribution.
Topic 9: Poisson Distribution & Moments
๐ฅ Poisson Distribution
Rare economic events and moment-generating function applications with Poisson distribution.
Topic 10: Tchebysheff's Theorem (Discrete)
๐ฅ Tchebysheff's Theorem
Risk bounds and probability inequalities in finance.
Topic 10b: Moment Generating Functions
๐ฅ Moment Generating Functions
MGF theory and applications to portfolio risk management
Unit 5: Continuous Random Variables
Topic 11: Continuous Probability Distributions
๐ฅ Continuous Random Variables
Continuous economic variables and probability density applications
Topic 12: Expected Values & Uniform Distribution
๐ฅ Expected Values & Uniform Distribution
Random pricing models and uniform distribution applications
Topic 13: Normal Probability Distribution
๐ฅ Normal Probability Distribution
Stock returns modeling and the bell-shaped curve in financial data analysis
Topic 14: Gamma Distribution
๐ฅ Gamma Distribution
Waiting time modeling and insurance claim applications with Gamma distribution
Unit 6: Multivariate Distributions
Topic 15: Multivariate Probability Theory
๐ฅ Multivariate & Bivariate Distributions
Joint probability models for economic variables
Topic 16: Independence & Covariance
๐ฅ Independence & Covariance
Portfolio correlation and risk diversification modeling
๐ Assessment Strategy & Academic Standards
WebWork Platform Integration
All assessments conducted through the WebWork platform with immediate feedback and adaptive learning
๐ Assessment Timeline
Quizzes
Homework
Midterm Exam
Final Exam
๐ฏ Grading Scale
โญ Student Evaluations - Fall 2025
Anonymous student feedback from 75 respondents collected at the end of Fall 2025 semester. These evaluations reflect student perceptions of course quality, instructor effectiveness, and overall learning experience.
๐ Rating Distribution
Teacher Effectiveness Metrics
Attendance Distribution
๐ฌ Student Insights & Themes
โจ Key Strengths
- Real-world applications: Students consistently praised the connection to economics and business contexts
- Clear explanations: Multiple students noted the instructor's ability to simplify complex concepts
- Instructor availability: High marks for being accessible and responsive to student questions
- Engaging teaching style: Students found lectures interesting despite challenging material
๐ฏ Areas for Improvement
- Pacing: Some students felt lectures moved quickly through material
- Assessment time: A few students mentioned time constraints on exams
- Major-specific examples: Request for more business-focused applications
- Lecture organization: Occasional feedback about connecting concepts more clearly
๐ฃ๏ธ Selected Student Quotes
"Mr Samir is able to explain complex materials, theorems and concepts in a very easy and intuitive way. You UNDERSTAND statistics in this course, not memorize."
"Absolutely. To be quite honest Prof Samir is one of the few instructors I've met whom genuinely care about his students... His classes are probably the only part of the day I actually enjoy learning."
"Yes, I would recommend this course to other students. It is very interesting and useful course. Also, I would like mention that this course becomes more interesting for me thank to our instructor. He taught us that how we can use this information in our real life."
"Of course, Samir muellim is one hell of a smart guy and whenever I mailed him he always explained the questions to me. He is probably the kindest instructor at the whole ADA!!"
"Yes because it's the best in explaining statistical analysis and application in real world"
๐ Detailed Ratings (1-5 Scale)
| Metric | Average | Mode | % Rating 4-5 |
|---|---|---|---|
| Overall Course Assessment | 4.56 | 5 | 97% |
| Exercise Sessions Quality | 4.45 | 5 | 93% |
| Lecture Quality | 4.61 | 5 | 96% |
| Real-life Economics Connection | 4.15 | 4, 5 | 87% |
| Teacher: Organization & Preparation | 4.69 | 5 | 96% |
| Teacher: Student Participation | 4.68 | 5 | 95% |
| Teacher: Availability | 4.73 | 5 | 96% |
| Teacher: Clarifying Difficult Material | 4.75 | 5 | 97% |
| Course Demand (vs other courses) | 3.88 | 4 | 77% |
๐ View Full Evaluation Data
Complete anonymized evaluation data including all student responses is available for download:
Data includes 75 student responses across 14 evaluation questions with both quantitative ratings and qualitative feedback.
๐ Course Literature
Primary Text 1
Mathematical Statistics with Applications
Authors: Wackerly, D. D., Mendenhall, W., & Scheaffer, R. L.
Edition: 7th Edition (2008)
Publisher: Cengage Learning
Primary Text 2
A First Course in Probability
Author: Ross, S. M.
Edition: 8th Edition (2010)
Publisher: Pearson Prentice Hall
โ๏ธ Technical Notes for Interactive Lectures
Optimal Experience
Use fullscreen mode (F11) for mathematical visualizations
Navigation
Arrow keys or on-screen buttons for slide progression
Requirements
Modern browser with JavaScript enabled, WebWork platform access
Mathematical Tools
Built-in calculators for combinatorics, probability, and distribution functions
Assessment Integration
Interactive exercises synchronized with WebWork assignments
Academic Integrity
All coursework conducted in accordance with ADA University Honor Code standards