Probability 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, goodness of fit

Introduction to statistical learning

Confidence intervals of Mean and Proportion; t-distribution

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

One sample t-test

The final grade of the course consists of the following components:

- Midterm (50%)

- Endterm (50%)

Final grade calculation: (0.5 * Midterm + 0.5 * Endterm)

Repair possibilities:

- Resit in next quarter

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

In case of insufficient results a repair option may exist in accordance with Article 2, Examination requirements, Clause 4, of the Implementation Regulations 2024-2025.