Course syllabus - Probability Theory and Statistical Inference

Objectives

The course presents basic concepts and methods of probability theory and statistical inference, and provides increased skills in application of these disciplines in science, technology and economics.

Learning outcomes

At the end of the course the student is expected to be able to
- formulate and apply basic concepts and laws for probability, in particular, sample point, event and sample space; the probability definition, independent events and conditional probability; basic properties of probability, the Law of Total Probability and Bayes' rule.
- formulate and apply basic properties and functions of random variables (both one- and two-dimensional).
- formulate definition of and apply following distributions: the geometric distribution, the uniform distribution, the binomial distribution, the hypergeometric distribution, the Poisson distribution, the exponential distribution and the normal distribution.
- describe and apply measure of central tendency, dispersion and dependency.
- describe and apply the main methods and concepts of point estimation, confidence intervals estimation, hypotheses testing and linear regression models.

Course content

Probability:
Basic concepts. Discrete and continuous random variables. Functions of random variables. One- and twodimensionella distributions. Measure of central tendency, dispersion and dependency. Geometric distribution, binomial distribution, hypergeometric distribution, Poisson distribution, uniform distribution, exponential distribution and normal distribution. Approximations to binomial distribution, Poisson distribution and hypergeometric distribution. The Central Limit Theorem.
Statistical Inference:
Estimation. The Method of Least Squares. The Method of Maximum Likelihood. Confidence Intervalls. Hypothesis Testing (incl. Chi-square test). Linear Regression.

Tuition

Lecture combined with exercises.

Specific requirements

Caculus II 7,5 credits or equivalent.

Examination

Written examination (TEN2), 3.5 credits, marks 3, 4 or 5
Written examination (TEN3), 4 credits, marks 3, 4 or 5

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass with credit, Pass, Fail