Probability Theory

COURSE OBJECTIVE
The learning objectives are as follows:

1. Knowledge and understanding of basic concepts of probability theory and probability distributions.
2. Selecting an appropriate method to solve typical problems in probability theory and applying these methods correctly.
3. Translating verbally described problems in the language of probability theory to solve the problem.
4. Knowledge of probability distributions which occur most commonly in practice and being able to use the known properties of these distributions to solve problems.

COURSE CONTENT
The mathematical foundation for both modeling decisions under uncertainty when performing statistics is the probability and the probability therefore has a central role in the bachelor Econometrics and Operations Research.

The structure of this course is as follows.
• Basic elements of the probability account (random experiment, outcomes space, eventuality and opportunity) and fundamental calculation rules for opportunities on eventualities. Combinatorial probability models, conditional probabilities, the rule of Bayes, and the law of total probability.
• Introduction of the concept of a stochastic variable, and concepts such as distribution function, probability function, expectation and variance of a stochastic variable.
• Specific discrete probability distributions, such as the binomial, hypergeometric, Poisson, and geometric distribution.
• Continuous stochastic variables and associated probability distributions. Specific continuous probability distributions such as the uniform, normal, exponential and gamma distribution. Relations between these continuous probability distributions and the previously introduced discrete probability distributions are discussed.
• If there is sufficient time at the end of the course, the concepts of bivariate and multivariate probability distribution included related concepts such as joint and marginal distribution functions, conditional probability distribution and independence of stochastic variables.

TEACHING METHODS
Lectures, tutorials

TYPE OF ASSESSMENT
Interbetween exam
Final exam
Individual assignment