1. The student knows and can apply elementary probability theory, like conditional probabilities and independence.
2. The student knows about the probability distribution of one random variable and their characteristics, like expectation and variance, and can calculate probabilities and measures in practical examples.
3. The student knows basic distributions for numbers (discrete) and interval variables (continuous), among others the normal and binomial distribution and recognizes these and can apply them in described practical situations.
4. The student can apply probability theory on joint and conditional discrete variables, including the computation of correlation coefficient and determination of the distribution of a function of discrete and continuous variables.
5. The student can determine expectations and probabilities for sums and means of independent variables, especially for normally distributed variables and can apply the central limit theorem for large samples in case of binomial and other non-normal distributions.
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Sample space, event, axioms of Kolmogorov, combinatorial probability, conditional probability, Bayes` rule, independence, random variable, expectation, variance, standard deviation, density, (cumulative) distribution function and distributions: binomial, hypergeometric, geometric, Poisson, exponential, uniform and normal, joint and conditional distributions, correlation, the distribution of the sum and the mean of independent variables, the Central Limit Theorem and its applications such as the normal approximation of binomial probabilities.
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