Engineering Probability and Statistics
This course introduces students to the foundational principles of probability and statistics, tailored for applications in embedded systems engineering. Students will learn how to collect, analyze, interpret, and present data using various statistical tools and techniques. Topics include descriptive statistics, probability distributions (discrete and continuous), hypothesis testing, confidence intervals, regression analysis, and an introduction to statistical process control. The emphasis is on understanding the theoretical underpinnings and applying these concepts to real-world engineering problems. The course aims to equip future embedded systems engineers with the analytical skills necessary for data-driven decision making, system reliability assessment, and quality assurance. Through practical exercises, laboratory simulations, and case studies, students will gain proficiency in using statistical software to solve complex engineering challenges. By the end of this course, students will be able to evaluate system performance, predict component failures, and optimize design parameters based on statistical evidence.
Prerequisites
Course outline
Lectures, virtual labs, and graded assignments — completed in your browser.
Syllabus
### Course Outcomes Upon successful completion of this course, students will be able to: 1. Apply fundamental concepts of probability and statistics to engineering problems. 2. Calculate and interpret descriptive statistics for various datasets. 3. Utilize discrete and continuous probability distributions to model random phenomena relevant to embedded systems. 4. Perform hypothesis tests and construct confidence intervals to draw statistically sound conclusions from data. 5. Apply linear regression techniques to model relationships between engineering variables. 6. Understand basic principles of statistical process control and reliability analysis. 7. Use statistical software to analyze data and present findings effectively. ### Weekly Topic List * **Week 1:** Introduction to Statistics and Data Analysis; Descriptive Statistics * **Week 2:** Basic Probability; Conditional Probability and Bayes' Theorem * **Week 3:** Discrete Probability Distributions (Binomial, Poisson, Hypergeometric) * **Week 4:** Continuous Probability Distributions (Normal, Exponential, Uniform) * **Week 5:** Joint Probability Distributions; Central Limit Theorem * **Week 6:** Statistical Estimation: Point and Interval Estimates; Confidence Intervals * **Week 7:** Hypothesis Testing: One-Sample Tests for Means and Proportions * **Week 8:** Hypothesis Testing: Two-Sample Tests for Means and Proportions * **Week 9:** Simple Linear Regression: Model, Estimation, and Inference * **Week 10:** Multiple Linear Regression: Introduction and Interpretation * **Week 11:** Analysis of Variance (ANOVA): One-Way * **Week 12:** Introduction to Reliability Engineering and Life Data Analysis * **Week 13:** Comprehensive Midterm Review * **Week 14:** Statistical Process Control (SPC) and Quality Improvement; Final Review ### Grading Policy * Knowledge Checks: 15% * Assignments/Labs: 30% * Quizzes: 25% * Final Exam: 30% ### Required Materials * Textbook: *Probability & Statistics for Engineers & Scientists* by Walpole, Myers, Myers, and Ye. (Latest Edition) * Statistical Software: Access to R or Python with relevant statistical libraries (e.g., NumPy, SciPy, Pandas, Matplotlib, Seaborn). * Scientific Calculator.