Probabilistic Methods and Statistics

obowiązkowe

Algebra liniowa z geometrią analityczną 420-IS1-1ALG
Analiza matematyczna 2 420-IS1-1AM2
Analiza matematyczna 3 420-IS1-2AM3

w sali

Random variable. Discrete probability. Continuous probability. Probability distributions. Expected values, variance, standard deviation. Stochastic processes. Sampling. Estimation. Hypothesis testing. Correlation and regression. Computer methods of statistics.

Course profile: General Academic

Form of study: Full-time studies

Course type: Obligatory

Field of science: natural sciences,

Discipline of science: mathematics

Year/semester of study: year 2/semester 4

Prerequisites (sequential system of courses and exams): Mathematical Analysis 2, Mathematical Analysis 3, Linear Algebra with Analytic Geometry

Lecture: 30 hours, Exercises classes: 30 hours, Laboratory classes: 15 hours,

Teaching methods: delivery method: lecture, searching methods, i.e. problem-based, situational, exchange of ideas, accounting exercises, laboratories, consultations, work with literature, solving homework tasks, discussions in problem groups.

ECTS credits: 5

Balance of student workload:

Class attendance:

- lecture 30 hours

- exercises classes 30 hours

- laboratory classes 15 hours

Course preparation:

- lecture 5 hours

- exercises 5 hours

- laboratory classes 5 hours

Literature study: 5 hours

Reports, homeworks: 10 hours

Preparation for the test: 15 hours.

Preparation for tests, the exams: 8 hours

Exam duration: 4 hours

Individual consultation with the teacher: 2 hours

Student workload:

- student workload related to the activities requiring the teacher's direct participation: 81h, 3 ECTS

- student workload that does not require the teacher's direct participation: 53h, 2 ECTS

1. Borovkov A.A., Probability Theory, Springer 2013.

2. Klenke A., Probability Theory. A Comprehensive Course, Springer 2020.

3. Shao J., Mathematical Statistics: Exercises and Solutions, Springer 2005.

4. Shao J., Mathematical Statistics, Springer Texts in Statistics, Springer 2003.

1. The student knows the basic concepts, definitions and theorems in the theory of probability - KA6_WG2.

2. The student knows the basic concepts of mathematical statistics and methods of statistical inference - KA6_WG2.

3. The student uses the concept of probabilistic space; is able to build and analyze a mathematical model of a random experiment - KA6_UW3.

4. The student can give various examples of discrete and continuous probability distributions and discuss selected random experiments and mathematical models in which these distributions occur. Knows the practical applications of basic distributions - KA6_UW3.

5. The student can use the formula for the total probability and Bayes' formula - KA6_UW3.

6. The student can determine the parameters of the distribution (discrete and continuous); can use limit theorems and laws of large numbers to estimate probabilities - KA6_UW3.

7. The student can use statistical characteristics of the population and their sample equivalents - KA6_UW3.

8. The student can make simple statistical inferences, also with the use of computer tools - KA6_UW3.

9. The student can use computer programs in the field of data analysis - KA6_UW3.

10. The student knows the limitations of his own knowledge and understands the need for further education - KA6_UU1.

Final assesment: exam.