Probability theory and statistics 1000-213bRPS
* Probability space: axioms of probability; properties of probability spaces; classical definition of probability; probability measures.
* Conditional probability and independence: definition of conditional probability, Law of Total Probability, Bayes' Theorem, independence of events.
* Discrete random variables: definition, properties, basic probability distributions - two-point, binomial, Poisson, geometric.
* Basic probability distributions: Bernoulli, binomial, Poisson, geometric, normal, exponential.
* Parameters of probability distributions: expected value, variance, higher moments.
* Inequalities and limit theorems: Markov Inequality, Chebyshev Inequality, Law of Large Numbers, Central Limit Theorem.
* Continuous random variables: definition, properties, exponential and normal distributions, Central Limit Theorem.
* Markov chains: definition and basic properties, classification of states, ergodicity, applications.
* Descriptive statistics: features and their scales, raw and cumulative data, graphical presentation, measures of central tendency and dispersion.
* Statistical reasoning: samples, statistics and estimators, parametric vs nonparametric estimation, maximum likelihood method.
* Hypothesis testing and confidence intervals: confidence intervals for the mean, confidence levels and p-values, methodology of a statistical test.
Type of course
Learning outcomes
Knowledge:
1. Has knowledge in the area of mathematics, involving probabilistic methods and statistics (especially discrete methods) (K_W01).
2. Understands the basic probabilistic techniques used in algorithm design (K_W02).
Abilities
1. Is able to formalize given random events using probabilistic spaces (K_U09).
2. Is able to conduct statistical analysis using available computer programs (K_U05).
Competences
1. Knows the and understands the need of further education (K_K01).
2. Is able to manage their time, undertake responsibilities and fulfill time constraints (K_K05).
Assessment criteria
The following elements are required:
- A partial exam during the semester.
- A lab project in statistics: It is required to write 4 programs in the language Python. This projects verifies the student's ability to perform a statistical analysis in practice.
- Exam. Exam consists of a theoretical test, and problems. To attend the first term, one needs to pass the partial exam and the lab project before the deadline. To attend the second term, one needs to pass the lab project before the exam in the second term.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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