Statistics for Engineers, 7.5 Credits

Contents

Module 1 (3 ECTS): Basic Probability Theory.
The notions probability, discrete and continuous random variable, probability function, probability density function, cumulative distribution function, expected value, variance, standard deviation, covariance and correlation, are defined. Furthermore, the most common probability distributions for technical applications are treated, with special emphasis on the normal distribution, distributions for linear combinations of normally and non-normally random variables (in the latter case applying the central limit theorem), and approximations of expected values and variances for non-linear functions of random variables.

Module 2 (3 ECTS): Basic Inference Theory with special emphasis on Technical applications.
The notions point estimate, unbiasedness, efficiency, hypothesis, significance level, power, type I and II errors, rejection region, p value and confidence level, are defined. The t-, Chi2-, and F-distributions are applied for hypothesis testing and interval estimation for one and two samples. During the course the sign test, Wilcoxon's two sample test, the analysis of contingency tables, basic analysis of variance, and simple and multiple regression analysis, are covered.

Module 3 (1.5 ECTS): Computer Labaorations using Statistical Software.

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

• account for the basic notions and laws from probability theory, that are included in the course
• account for the basic notions from inference theory, that are included in the course

Skills

• summarize the results from a statistical study in written form
• apply probability-, probability density- and cumulative distribution functions in order to calculate probabilities, expected values, variances, and standard deviations for random variables
• apply the central limit theorem for probability calculations for linear combinations of random variables.
• set up appropriate null- and alternative hypotheses for conducting statistical tests
• analyze data with the statistical methods in the course, with as well as without the assistance of statistical software

Judgement and Approach

• valuate the results from a statistical study and draw relevant conclusions
• through judgements, and with account to relevant scientific and ethic aspects, decide what statistical methods are suitable for the analysis of existing data

Required Knowledge

The course requires 15 ECTS in Mathematics including derivatives and integrals, or corresponding.

Form of instruction

The teaching is in the form of lectures, group sessions and computer lab supervision.

Examination modes

Modules 1 and 2 are assessed through written exams. Module 3 is assessed through oral and written presentations of computer lab reports. For the exams, one of the following judgements are awarded: Failed (U), Passed (3), Passed with merit (4) or Passed with distinction (5). For Module 3 one of the judgements Failed (U), Passed (G) is awarded. For the course as whole, one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). To pass the whole course, all modules must have been passed. The grade is decided from the mean of the exam scores, and is only set once all compulsory elements have been assessed.

Deviations from the syllabus examination form can be made for a student who has a decision on pedagogical support due to disability. Individual adaptation of the examination form shall be considered based on the student's needs. The examination form is adapted within the framework of the expected learning outcomes of the course syllabus. At the request of the student, the course coordinator, in consultation with the examiner, must promptly decide on the adapted examination form. The decision shall then be communicated to the student.

A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Credit transfer
All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå University, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications

Other regulations

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering.