Before choosing course

The overall purpose of the course is that the student should be well acquainted with basic concepts, theory, models and solution methods in probability theory and statistical inference.

Course offering missing for current semester as well as for previous and coming semesters

Content and learning outcomes

Course contents

Basic concepts like probabilities, conditional probabilities and independent events. Discrete and continuous random variables, especially one dimensional random variables. Measures of location, scale and dependency of random variables and data sets. Common distributions and models: normal, binomial and Poisson distribution. Central limit theorem and Law of large numbers.

Descriptive statistics.

Point estimates and general methods of estimation as the method of maximum likelihood and least squares. General confidence intervals but specifically confidence intervals for mean and variance of normally distributed observations. Confidence intervals for proportions, difference in means and proportions.

Testing statistical hypothesis. Choice of significance level and power. Chi2-test of distribution, test of homogeneity and contingency. Simple and multiple linear regression.

Intended learning outcomes

To pass the course, the student should be able to do the following:

• construct elementary statistical models for experiments
• describe standard models and explain the applicability of the models in given examples
• define and calculate descriptive quantities like expectation, variance, and percentiles for distributions and data sets.
• with standard methods calculate estimates of unknown quantities and quantify the uncertainty in these estimates
• value and compare methods of estimation
• analyse how measuring accuracy affect conclusions and quantify risks and error probabilities in statistical analysis
• design test and select sample sizes so that desired precision of estimates and significance level and power of tests are achieved

• Combine all the concepts and methods mentioned above in order to solve more complex problems.

Course Disposition

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Literature and preparations

Specific prerequisites

Basic courses in differential and integral calculus. Basic course in linear algebra.

Recommended prerequisites

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Equipment

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Literature

Blom et al. Sannolikhetslära och statistikteori med tillämpningar. Studentlitteratur.
Complemental material from the department.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

Examination

• TEN1 - Examination, 7,5 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Written exam.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Examiner

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Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

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SCI/Mathematics

Technology

First cycle