- Student can reason on stochastic experiments and use sample space, events, and set theoretical operators to describe events.
- Student can reason about and use the axioms of probability theory, Laplace and the frequency interpretation.
- Student can use the basic principle of counting, and use especially the binomial coefficient.
- Student can reason about and use the concept of independent events.
- Student can use discrete and continuous random variables.
- Student can apply selection of probability mass functions/probability density functions and calculate expected value, variance and moments.
- Student can apply Chebyshev’s inequality.
- Student can determine and use the cumulative distribution function.
- Student can determine the probability density function of a transformed random variable.
- Student can reason about and use conditional probabilities, in particular Bayes’ rule.
- Student can use joint discrete and continuous random variables, in particular marginal probability mass/density functions.
- Student can calculate conditional expectation, in particular continuous random variables given a discrete random variable.
- Student can use functions of two discrete/continuous random variables.
- Student can determine the probability mass/density function of use the sum of two random variables.
- Student can determine the covariance of two random variables.
- Student can determine the correlation coefficient of two random variables.
- Student can apply the (standard) normal distribution.
- Student can apply the central limit theorem.
Additionally, there will be two 4 hour statistical inference lab sessions in which students are presented with highlights from statistical inference topics.
- Student can estimate the mean and variance of a given set of numbers.
- Student knows the difference between estimator and estimate.
- Student understands the importance of properties of estimators: biasedness, consistency, asymptotic behavior.
- Student can apply the maximum likelihood estimation procedure.
- Student can determine confidence interval of estimated mean of Gaussian with known variance.
- Student can determine confidence interval of estimated mean of Gaussian with unknown variance.
- Student can use null and alternative hypotheses for two sided tests, under the assumption of a normal distribution with known variance.
- Student can apply regression for one or more independent variables.
- Student can interpret R2 as a measure for fit.
- Student can extend the least squares approach to nonlinear basis functions.
In probability theory you learn how to model events of chance and you learn some basic techniques to analyse those models. The following topics will be discussed: experiment, sample space and probability, basic combinatorial probability theory; conditional probability and independence; discrete and continuous random variables and their (joint) distributions and moments; the normal distribution and the central limit theorem.|
In the SI lab you will learn some topics from statistical inference (mean, std, parameter estimation, confidence intervals, hypothesis testing, linear regression).