- Describe and apply basic concepts of probability theory such as outcome, event, probability, conditional probability, independence, stochastic variable, distribution, distribution function, frequency function, density, expectation, moment, (co)variance, correlation coefficient and moment generating function.
- Adequately model chance events.
- Describe and use the most important discrete and continuous distributions and their properties.
- Describe and apply moment generating functions, the Markov and Chebyshev inequalities, the weak and strong laws of large numbers and the central limit theorem.
- Use the technique of conditioning for the computation of probabilities and expectations.
This course presents a mathematical foundation for the concepts associated with uncertainty and events of chance. In particular, you learn how to model events of chance as stochastic variables and some basic techniques to analyse those models. We do this both for discrete (the outcome of throwing a dice) as well as continuous (the time it takes you to drive home) variables. We relate different stochastic variables through concepts such as correlation and independence. We introduce the concepts of conditioning to model prior information. If we have stochastic variables, which are the sum of many independent stochastic variables, then we will show that in certain cases, we can simplify the model by using the laws of large numbers.