Elementary probability theory Field of study: Mathematics
Programme code: W4-S1MT19.2024

Buduje przestrzeń probabilistyczną do danego doświadczenia losowego i potrafi wyliczyć prawdopodobieństwa poszczególnych zdarzeń losowych. [WaRP_1]

Zna pojęcie prawdopodobieństwa warunkowego, niezależności zdarzeń oraz podstawowe fakty związane z tymi pojęciami. [WaRP_2]

Zna i rozumie pojęcie zmiennej losowej, jej rozkładu prawdopodobieństwa i dystrybuanty, a także zależności między nimi. Podaje przykłady rozkładów dyskretnych i absolutnie ciągłych. Oblicza wartość oczekiwaną i wariancję zmiennej losowej. [WaRP_3]

Zna pojęcie wektora losowego. Potrafi wyznaczać rozkłady brzegowe oraz badać niezależność zmiennych losowych. [WaRP_4]

Wyznacza rozkład sumy niezależnych zmiennych losowych. [WaRP_5]

Zna różne rodzaje zbieżności ciągów zmiennych losowych (m.in. prawie na pewno i stochastyczną). Weryfikuje czy ciąg zmiennych losowych spełnia mocne i/lub słabe prawo wielkich liczb. Stosuje centralne twierdzenie graniczne do szacowania prawdopodobieństw. [WaRP_6]

reviewing literature, documentation, tools and materials as well as the specifics of the syllabus and the range of activities indicated in it as required for full participation in classes

reading the literature indicated in the syllabus; reviewing, organizing, analyzing and selecting source materials to be used in class

activities involving the repetition, refinement and consolidation of practical skills, including those developed during previous classes or new skills necessary for the implementation of subsequent elements of the curriculum (as preparation for class participation)

agreeing on materials complementary to those indicated in the syllabus, supporting the implementation of tasks resulting from or necessary for class participation

developing, preparing and assessing the usefulness of tools and materials (e.g. aids, scenarios, research tools, equipment, etc.) to be employed in class or as an aid when preparing for classes

reading through the syllabus and getting acquainted with its content

consulting the content of the syllabus, possibly in the presence of the year tutor or members of the class group, and, if necessary, reassessing the provisions concerning special conditions for class participation, e.g., space and time requirements, technical and other requirements, including conditions for participation in classes outside the walls of the university, classes organized in blocks, organized online, etc.

devising a task implementation strategy embracing the division of content, the range of activities, implementation time and/or the method(s) of obtaining the necessary materials and tools, etc.

exploring the studied content, inquiring, considering, assimilating, interpreting it, or organizing knowledge obtained from the literature, documentation, instructions, scenarios, etc., used in class as well as from the notes or other materials/artifacts made in class

a set of activities aimed at performing an assigned task, to be executed out of class, as an obligatory phase/element of the verification of the learning outcomes assigned to the course

reading through the academic teacher’s comments, assessments and opinions on the implementation of the task aimed at checking the level of the achieved learning outcomes

reviewing and selecting tasks and activities enabling the elimination of errors indicated by the academic teacher, their verification or correction resulting in completing the task with at least the minimum passing grade