The pedagogy of the course is “problem-based learning”. There
will be introductory and summing up lectures and students will work
in small groups with assignments, problem solving, computer
simulations and case studies.
To provide the participants with both an intuitive and rigorous
understanding of probability theory, and to give them an
introduction to statistical thinking and methods. This is partly
done by exposure to a number of basic probabilistic/ statistical
models of widespread application. The course gives the mathematical
background for probabilistic methods used in stochastic processes
and in statistics. The participants also learn to handle a number
of elementary problems which occur frequently in engineering
practice and are thus enabled to critically assess probabilistic
and statistical investigations This enables the participants to
discuss a given scientific method and the possibility to follow a
research and development effort.
Læringsmål:
En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:
Apply basic definitions and axioms of probability in problem
solving.
Apply the concepts of conditional probability and conditional
distribution.
Formulate simple probability models from verbal
descriptions.
Identify and describe probability distributions, including
Poisson, binomial, exponential and the normal distribution.
Choose a suitable probabilistic model for a real world
phenomenon.
Make calculations involving distributions, expectations,
moments and correlations.
Estimate and interpret simple summary statistics, such as mean,
standard deviation, variance, median and quartiles.
Apply simple graphical techniques, including histograms.
Apply and interpret important statistical concepts, such as the
formulation of models, parameter estimation, construction of
confidence intervals and hypothesis testing.
Understand and interpret output from some commonly used
statistical software.
Document technical calculations in a written form, both
compactly and precisely.
Work within a group and cooperate to solve homework
assignments.
Kursusindhold:
Axioms of probability theory, elements of combinatorial analysis,
conditional probability, independence, Bayes' rule, random
variables, expectation, the binomial distribution, normal
approximation to the binomial distribution, sampling with and
without replacement, the hyper-geometric distribution, the
geometric and negative binomial distributions, the Poisson
distribution, cumulative distribution function, the normal,
exponential, and gamma distributions, the chi-squared distribution,
random number generation, Markov and Chebychev inequalities, law of
large numbers, functions of random variables, joint distributions,
the central limit theorem.
Simple methods for graphical and tabular assessments of collected
or
measured data. Hypothesis testing, estimation of parameters, and
construction of confidence intervals in common situations
(especially mean values, variances, and proportions). Model
formulation. Model control: goodness-of-fit test and test for
independence. Examples of applications in the engineering
sciences.
Litteraturhenvisninger:
- Lecture notes on CampusNet.
Bemærkninger:
This course is an integrated part of the study program in
Mechanical Engineering. It is, however, a general methodological
course aimed at all engineering students, regardless of
specialization.
