Probabilistic Methods and Statistics 510-IS1-2PST-ENG
Wykład (WYK) Rok akademicki 2023/24

The student knows the basic concepts, definitions and theorems in probability - exam and/or short tests.

The student knows the basic concepts of mathematical statistics and methods of statistical inference - exam and/or short tests.

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 - exam.

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

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

The student knows the limitations of his own knowledge and understands the need for further education - evaluation of the student's activity during classes.

1. The student who has obtained a credit for exercises classes and laboratoriy classes is admitted to the exam.

2. There are short tests during all lectures. The student may receive 10 points for all short tests. Scoring and completing short tests takes place in accordance with the rules applicable to completing the exercises, except that in the event of being late or absent from the lecture where the short test was taken, the student gets 0 points for it.

3. The exam consists of two parts:

• practical,

• theoretical.

The student may receive 70 points from the exam. Each part of the exam is assessed by the tutor on the appropriate point scale, but the final result is converted into the above-mentioned score with a precision of two decimal places.

a) There is a possibility of exemption from each part of the exam. The exemption can be used by a student who

-did not cheat on an tests and short tests

-obtained at least 90% of the points on

* tests during the exercise classes (in the case of the practical part)

* short tests during the lectures (in the case of the theoretical part).

b) The exemption thresholds indicated in the previous point are subject to change.

c) The student dismissed from a given part of the exam receives a number of points in a given part proportional to the number of points obtained from tests or short tests, respectively.

4. The basis for issuing the final grade for the exam is the total sum of points obtained from: the practical and theoretical part of the exam, short tests during lectures and 10% of the points obtained during classes and laboratory. The final grade is consistent with the following scale of grades.

Grading scale:

• unsatisfactory (fail) (ECTS grade F/FX, Polish grade 2) - up to 50.99 points,

• satisfactory (ECTS grade E, Polish grade 3) - from 51.00 to 60.99 points,

• better than sufficient (ECTS grade D, Polish grade 3+) - from 61.00 to 70.99 points,

• good (ECTS grade C, Polish grade 4) - from 71.00 to 80.99 points

• better than good (ECTS grade B, Polish grade 4+) - from 81.00 to 90.99 points,

• very good (ECTS grade A, Polish grade 5) - from 91.00 points.

1. Probabilistic space - axiomatic approach to probability.

2. Conditional and total probability, Bayes' theorem, independence.

3. One-dimensional discrete and continuous random variables, the cumulative distribution function, moment and others parameters, independence.

4. Multidimensional random variables.

5. Selected inequalities for moments of random variables.

6. Laws of large numbers and the central limit theorem.

7. Fundamental concepts of mathematical statistics.

8. Estimation: point and interval.

10. Testing statistical hypotheses: selected parametric and non-parametric tests.

11. Selected problems from the theory of stochastic processes.

Teaching methods: lectures, consultations, literature study.