Download Probability and Statistics

Course
Specifications
Valid as from the academic year 2017-2018
Probability and Statistics (E003042)
Course size
Credits 4.0
(nominal values; actual values may depend on programme)
Study time 120 h
Contact hrs
72.5 h
Course offerings and teaching methods in academic year 2017-2018
A (semester 2)
seminar: coached exercises
22.5 h
lecture
22.5 h
guided self-study
30.0 h
Lecturers in academic year 2017-2018
De Cooman, Gert
TW06
lecturer-in-charge
Offered in the following programmes in 2017-2018
crdts
Bachelor of Science in Civil Engineering
4
Bachelor of Science in Computer Science Engineering
4
Bachelor of Science in Chemical Engineering and Materials Science
4
Bachelor of Science in Electrical Engineering
4
Joint Section Bachelors of Science in Engineering
4
Bachelor of Science in Engineering Physics
4
Bachelor of Science in Electromechanical Engineering
4
Preparatory Course Master of Science in Biomedical Engineering
4
Preparatory Course European Master of Science in Nuclear Fusion
4
and Engineering Physics
Preparatory Course Master of Science in Engineering Physics
4
offering
A
A
A
A
A
A
A
A
A
A
Teaching languages
Dutch
Keywords
probability theory, statistics, probability distributions
Position of the course
To teach the students the basic principles and the reasoning methods of probability
theory. To familiarise them with the most commonly used probabilistic and statistical
techniques, and the ideas behind them. To teach them how to apply statistical methods
using both pen-and-paper methods and more advanced Python tools.
Contents
• Introduction: Practical information about the course, What is probability theory?,
• Where is probability theory applied?, What is statistics?
• Introduction to probability: Different interpretations, Events and sets, Definition and
• basic properties, Finite sample spaces
• Conditional probability: Definition and Bayes's Rule, Multiplication rule, Inverse
• probability and Bayes's Theorem, Independent events
• Random variables and their distributions: Definition, The distribution of a random
• variable, Discrete random variables and their distribution, Continuous random
• variables and their distribution, Distribution functions and fractiles, Higher• dimensional random variables, Joint distributions, Marginal distributions, Conditional
• distributions, Tranformations of random variables
• Expectations: Definition and basic properties, Expectations and probabilities,
• Conditional expectations, Expectations and independent random variables, Variance,
• covariance and correlation, Moments, Moment generating function and characteristic
(Proposal)
1
• function, Chebyshev's inequality, Law of large numbers
• Special discrete distributions and their applications: Bernoulli distribution, Binomial
• distribution, Hypergeometric distribution, Geometric distribution, Poisson distribution
• Special continuous distributions and their applications: Continuous uniform
• distribution, Exponential distribution, Gamma distribution, Normal distribution and the
• Central Limit Theorem, Two-dimensional normal distribution, Chi-squared distribution
• Descriptive statistics and sampling: Sampling and experiments, Ordering and
• representing data, Sample statistics from data, Samples and their statistics as
• random variables
• Estimations: Definitions and basic properties, Likelihood function, Maximum
• likelihood estimators, Method of Moments, Confidence intervals
• Linear regression: Terminology, Simple linear regression using least squares,
• Distribution of the regression coefficients
Initial competences
Basis Mathematics Tools [elementary functions (exponential, logarithm), limits,
matrices, factorials, combinations and permutations], Mathematical Analysis I [functions
of a single variable, derivatives, integrals, series], Mathematical Analysis II [functions of
several variables, partial derivatives, double integrals].
Final competences
1 To reason and to work with multi-dimensional random variables.
2 To calculate probabilities of events and expectations of random variables
3 To identify an appropriate probabilistic model for the analysis of an event or
1 experiment.
4 To interpret and to judge the results of statistical sampling, and to represent them in
1 an appropriate form.
5 To understand and to apply methods for (parameter) estimation
6 To perform a linear regression and to interpret its results.
Conditions for credit contract
Access to this course unit via a credit contract is determined after successful competences
assessment
Conditions for exam contract
This course unit cannot be taken via an exam contract
Teaching methods
Guided self-study, lecture, seminar: coached exercises
Learning materials and price
Lecture notes and additional course material through Minerva.
Textbook in English (price around 70 euros): Probability and Statistics, Morris H.
DeGroot en Mark J. Schervish, Pearson International Edition (4th Edition), ISBN-13:
978-0-321-70970-7, ISBN-10: 0-321-70970-5
References
• Probability and Statistics, Morris H. DeGroot en Mark J. Schervish, Pearson
• International Edition (4th Edition), ISBN-13: 978-0-321-70970-7, ISBN-10: 0-321• 70970-5
• Probability & Statistics for Engineers & Scientists, Walpole, Myers, Myers and
• Ye, Pearson International Edition (9th Edition), ISBN-13: 978-0-321-74823-2, ISBN• 10: 0-321-74823-9
Course content-related study coaching
The lecturers and assistants are available before and after the lectures. Individual
coaching by the lecturer as scheduled. Additional individual coaching by the tutoring
cell by appointment.
Evaluation methods
end-of-term evaluation and continuous assessment
Examination methods in case of periodic evaluation during the first examination period
Written examination with multiple choice questions, written examination
Examination methods in case of periodic evaluation during the second examination period
Written examination with multiple choice questions, written examination
Examination methods in case of permanent evaluation
Written examination, open book examination
(Proposal)
2
Possibilities of retake in case of permanent evaluation
examination during the second examination period is not possible
Extra information on the examination methods
• Periodic evaluation: Written closed-book examination.
• Continuous assessment: 2 written tests (open book), dates announced in advance
Calculation of the examination mark
continuous assessment:
• The scores of the two tests (each marked out of 20), T1 and T2 result in the score T’
• using a weighted average for the tests (40% and 60%): T'= 0,4 T1 + 0,6 T2
• Application of a pass fail system results in the final score T for the tests: T=20 if T' is
• no less than 10, and T=T' if T' is less than 10.
• The variable A represents how many times the student was absent without good
• cause (0, 1 or 2).
• periodic evaluation:
• Taken the exam results in a score E (marks out of 20).
The final mark thus is:
In the first examination period
• Max(0,25 T + 0,75 E, 0,1 T + 0,9 E) -2A if E is at least 8
• E-2A, if E is less than 8
In the second examination period
• Max(0,25 T + 0,75 E,E) if E is at least 8
• E, if E is less than 8
(Proposal)
3