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

The student is able to use statistical and probabilistic methods to analyze data - tests and/or homework, evaluation of the student's activity during classes.

The student uses the concept of a probabilistic space; is able to build and analyze a mathematical model of a random experiment - tests and/or homework, evaluation of the student's activity during classes.

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 timetables - tests and/or homework, evaluation of the student's activity during classes.

The student can use the formula for the total probability and the Bayes formula - tests and/or homework, evaluation of the student's activity during classes.

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 - tests and/or homework, evaluation of the student's activity during classes.

The student can use statistical characteristics of the population and their sample counterparts - tests and/or homework, evaluation of the student's activity during classes.

1. The following written assignments are planned for the classes:

• tests, for which the student may receive 80 points,

• homework, for which the student may receive 20 points.

a. Each written work in a given group of works is scored equally, ie a number of points is assigned to it equal to the quotient of the number of points allocated for all the work and the number of all works. The tutor may evaluate each of the written assignments on the appropriate point scale, but the number of points obtained is converted into the number of points indicated in the syllabus with an accuracy of two decimal places.

b. The tutor sets one date for each test.

c. Each homework should be handed over to the tutor within two weeks of its assignment (in the event of the end of the semester, this deadline may be shortened to 1 week). In the event that the last day of the deadline for giving homework falls on a day off from classes, the homework should be submitted on the first day of classes immediately following that day. Works delivered after the deadline are not taken into account.

2. The basis for exempting a student from participation in part or all of the classes may be

• obtaining the consent of the Director of the Institute for the Individual Organization of Studies (IOS), unless the subject is included in the list of subjects for which the student is required to attend.

• participate in the Individual Study Program (IPS),

• class collisions due to subject repetition.

The method of conducting classes in the case of a student who has received the Director's of Institute consent for IOS or IPS should be agreed within 14 days of receiving this consent. Obtaining consent to be exempted from exercise is not possible after the deadline specified in the preceding sentence.

3. Missing the 6 hours of the exercises classes provided by the plan by the student without justifying them may be the basis for failing the classes.

4. The tutor issues a final grade in accordance with the grading scale specified at the end, provided that cheating on the test means obtaining a unsatisfactory grade from the laboratory.

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. Random events and probability. Probabilistic space.

2. Conditional probability and independence of events. Total probability and Bayes' theorem.

3. One-dimensional discrete and continuous random variable: distribution, cumulative distribution function, moments and others parameters of random variables.

4. Two-dimensional random variables: marginal and conditional distributions, moments.

6. Application of the central limit theorems.

7. Descriptive statistics.

8. Point and interval estimation: estimators, confidence intervals.

9. Verification of hypotheses: selected parametric and non-parametric tests of significance.

Teaching methods: exercises, consultations, literature study, homework assignments, discussions in groups.