Probability Theory and Statistics

• Graphical and numerical summaries of data

• Introduction to probability

• Some elementary combinatorics to find probabilities

• Conditional probability; Bayes' rule; stochastic (in)dependence

• Random variables; probability mass function; density function; distribution function

• Standard distributions: Binomial, Poisson, Geometric, Normal, Uniform, Exponential, Pareto

• Expectation and variance; transformations; Jensen's inequality

• Multivariate random variables; joint distributions; joint and marginal density functions; (in)dependence of random variables

• Covariance and correlation

• Chebychev's inequality; Law of Large numbers; Central Limit Theorem

• Sampling theory and statistical models; mean, sample variance, histogram, empirical distribution function, boxplot

• Theory of Estimators: Bias, Efficiency, Mean squared error

• Linear Regression: univariate and multivariate, categorical variables, goodness of fit

• Confidence intervals for Mean and Proportion; t-distribution

• Testing theory: Type I/II Error, p-value, significance level, critical region, multiple testing, p-hacking

• Hypothesis tests on mean(s), proportion(s), variance, regression parameters

The grade is completely determined by one single exam at the end of the course.

Repair possibility: resit in next quarter.

Permitted Materials during Test: Formula sheet (one sheet, to be made by the student) and a simple, non-programmable, non-graphical calculator.

Disclaimer: information may change depending on unforeseen circumstances or measures (see: TER Art 29, sub 4).