### 2016　Probability and Statistics for Engineering and Sciences

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School of Engineering
Instructor(s)
Daniel Berrar
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Mon9-10(W611)
Group
B
Course number
XEG.G301
Credits
2
2016
Offered quarter
3-4Q
Syllabus updated
2016/9/27
Lecture notes updated
-
Language used
English
Access Index

### Course description and aims

This course covers the fundamentals of probability and statistics, with a focus on applications from
engineering and the sciences. The course begins with an introduction to graphical data
representation and descriptive statistics. Topics in probability include discrete and continuous
random variables, probability rules, probability distributions, the law of large numbers, the central
limit theorem, and expected value. Topics in statistics include sampling distributions, estimation of
population parameters, confidence intervals, and significance testing. The course does not focus
exclusively on concepts from the frequentist paradigm, but also introduces elementary Bayesian
statistics. The goal of this course is that the students acquire a solid statistical literacy that enables
them to interpret statistical information and graphs. Students will also learn how to choose the
appropriate statistical methodologies and tools to analyze data scientifically. To achieve this goal, the
course includes many real-world examples from engineering and the sciences.

### Student learning outcomes

After successful completion of this course, the students will
(1) understand how to interpret various graphical representations of statistical information;
(2) understand the key elements of probability and statistics;
(3) be able to analyze data scientifically with the appropriate statistical methodologies and tools;
(4) be able to adequately communicate analytical results in an interdisciplinary environment.

### Keywords

bar chart; histogram; box-and-whiskers plot; mean; variance; standard deviation; quartile; sample
space; events; marginal probability; joint probability; conditional probability; random variable; Bayes
theorem; central limit theorem; law of large numbers; binomial probability distribution; normal
probability distribution; sampling distribution; confidence interval; significance testing; t-test.

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

Classes usually begin with a real-world example to motivate a statistical concept. This concept is then
formally described, and mathematical proofs are given where appropriate. Then, the instructor and
the students solve the real-world problem interactively during class. Classes are interactive, and
students' active participation is welcome.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction; organizing and graphing data; bar charts and histograms None.
Class 2 Measures of central tendency, dispersion, and position; box-and-whiskers plot Revise contents of previous class; complete assignment
Class 3 Sample space, events, and probability axioms Revise contents of previous class; complete assignment
Class 4 Marginal probability, joint probability, conditional probability Revise contents of previous class; complete assignment
Class 5 Multiplication and addition rules Revise contents of previous class; complete assignment
Class 6 Bayes' theorem and Bayesian statistics [1 of 2] Revise contents of previous class; complete assignment
Class 7 Bayes' theorem and Bayesian statistics [2 of 2] Revise contents of previous class; complete assignment
Class 8 Discrete random variables and expected value; law of large numbers Revise contents of previous class; complete assignment
Class 9 Discrete probability distributions, binomial probability distribution Revise contents of previous class; complete assignment
Class 10 Continuous random variables and continuous probability distribution, normal probability distribution Revise contents of previous class; complete assignment
Class 11 Applications of binomial and normal probability distribution Revise contents of previous class; complete assignment
Class 12 Central limit theorem, sampling distributions of sample mean and sample proportion Revise contents of previous class; complete assignment
Class 13 Estimating population parameters, confidence intervals Revise contents of previous class; complete assignment
Class 14 Fisherian and Neyman-Pearsonian paradigms of testing Revise contents of previous class; complete assignment
Class 15 Significance testing, tests for the mean, t-distribution Revise contents of previous class; complete assignment

### Textbook(s)

None required. Course materials are provided during class.

### Reference books, course materials, etc.

Mann P.S. (2013) Introductory Statistics. John Wiley & Sons, Singapore, ISBN: 978-1-118-31870-6.

### Assessment criteria and methods

Students' course scores are based on midterm and final exams.

### Related courses

• IEE.A204 ： Probability for Industrial Engineering and Economics
• IEE.A205 ： Statistics for Industrial Engineering and Economics

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Knowledge of elementary algebra and calculus is required.