2288.20 - Probability Theory and Statistics
Probability Theory and Statistics
Pass grade in Mathematics B at the upper secondary level. Skills and knowledge from or equivalent to those taught in the courses Mathematics 1 and Mathematics 2 is an advantage.
The aim of the course is to provide students with the basic ideas of probability and statistics required for the study of economics.
The first part of the course is an introduction to probability theory. The topics include probability, stochastic variables, probability distributions and transformations of stochastic variables. The students learn how to describe stochastic variables by their distributions. The students see examples of various probability distributions (discrete and continuous), and how one can describe these distributions with measures such as mean and variance. The second part of the course is an introduction to statistical analysis of data and inference. This includes choice of model to fit the data, estimating parameters in the model, testing hypotheses and drawing conclusions about the model assumptions.
Learning and teaching approaches
New material is presented in lectures and classes. In classes, students solve and present exercises.
Having successfully completed the course, the student will be able to describe and implement the following: • Tools used in descriptive statistics • Law of Large Numbers and Central Limit Theorem • Statistical concepts - including: o Joint, marginal and conditional probability o Stochastic variables and transformations of stochastic variables o Distributions o Probability function o Density function o Independent variables o Mean and conditional mean o Variance and covariance • Selected probability distributions, including: o Bernoulli, Binomial, Poisson, Multinomial, geometric, uniform, normal, chi2, and exponential distributions. • Important statistical concepts, including: o Independent, identically distributed variables o Likelihood function o Maximum likelihood estimator o Properties of maximum likelihood estimators including consistency and asymptotic normality o Confidence intervals and hypothesis tests
3 hour written exam. Students may use textbooks, notes and data programs during the exam. They may not use the internet. Students are required to pass a minimum of two assignments in order to attend the exam.