- 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.
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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).
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