In this course, firstly typical probability distributions and statistics are lectured after a short review of basic of probability. Secondly, estimation and verification of parameters are learned. Based on the knowledge of statistics, explanation of characteristics of population is studied.
A variety of knowledge on mathematics are required to resolve issues and make progresses in mechanical engineering. Probability and statistics is not only important for following a lot of courses in mechanical engineering, but also indispensable for data handling and evaluation in researches, developments and production after your graduation, especially in the era of big data. Students are expected to take this course.
By the end of this course, students will be able to:
1) Explain typical sample statistics and probability distributions
2) Calculate parameters by means of estimation and verification
3) Explain characteristics of target population by means of statistics.
Mean, standard deviation, sample, parameter, binominal distribution, Poisson distribution, normal distribution, probability density, maximum likelihood estimation, interval estimation
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
The course is taught in lecture style. Exercise problems will be assigned after the fourth class. Required learning should be completed outside of the classroom for preparation and review purposes.
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction, event and probability | Understand relation between data and sample space，definition of event and probability, Bayes' theorem |
Class 2 | Random variable and probability distribution | Understand random variable, probability distribution, probability density function |
Class 3 | Probability distribution, mean and standard deviation, central limit theorem | Understand mean and standard deviation, moment-generating function, normal distribution, central limit theorem |
Class 4 | Examples of probability distribution | Understand probability distributions such as binominal, Poisson and normal distributions |
Class 5 | Sample, statistic and sample distribution | Understand relation between sample and population，relation between sample statistics and parameter, χ2 and t distributions |
Class 6 | Estimation | Understand maximum likelihood estimation and interval estimation |
Class 7 | Statistical test | statistical test and typical statistics used in procedure of the test |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Materials will be provided if they are required.
Robert S. Witte, John S. Witte, "Statistics", Hoboken : John Wiley and Sons, Inc., (2015)
Students' knowledge of probability and statistics will be assessed.
Final exam 70%, exercise problems 30%.
Students are expected to have successfully completed both Calculus I (LAS.M101) and Calculus II (LAS.M105) or have equivalent knowledge.