Course detail
Probability and Statistics I
FSI-S1P Acad. year: 2024/2025 Summer semester
The course makes students familiar with descriptive statistics, random events, probability, random variables and vectors, probability distributions, random sample, parameter estimation, tests of hypotheses and statistical software Statistica. Seminars include solving problems and applications related to mechanical engineering.
Language of instruction
Czech
Number of ECTS credits
5
Supervisor
Department
Entry knowledge
Rudiments of the differential and integral calculus.
Rules for evaluation and completion of the course
Course-unit credit requirements: active participation in seminars, mastering the subject matter, passing both written exams and semester assignment acceptance.
Examination: Evaluation based on points obtained for semester assignment (0-10 points) and a test (0-90points). The exam test consists of two parts: a practical part (2 tasks from the theory of probability: probability and its properties, random variable, distribution Bi, H, Po, N and discrete random vector; 2 tasks from mathematical statistics: point and interval estimates of parameters, tests of hypotheses of distribution and parameters); a theoretical part (4 tasks related to basic notions, their properties, sense and practical use,and proofs of two theorems); evaluation: each task 0 to 15 points and each theoretical question 0 to 5 points; evaluation according to the total number of points (scoring 0 points for semestral assignment, any practical part task, any theoretical part task means failing the exam): excellent (90 – 100 points), very good (80 – 89 points), good (70 – 79 points), satisfactory (60 – 69 points), sufficient (50 – 59 points), failed (0 – 49 points).
Participation in the exercise is mandatory and the teacher decides on the compensation for absences.
Aims
The course objective is to make students majoring in Mathematical Engineering acquainted with methods of probability theory, descriptive and mathematical statistics, and with statistical software Statistica as well as to encourage students` stochastic way of thinking for developing mathematical models with the emphasis on engineering branches.
Students obtain needed knowledge from the probability theory, descriptive statistics and mathematical statistics, which will enable them to understand and apply stochastic models of technical phenomena and processes based upon these methods.
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's, compulsory
Programme C-AKR-P: , Lifelong learning
specialization CLS: , elective
Type of course unit
Lecture
26 hours, optionally
Syllabus
Random events, field of events, and probability (properties).
Conditioned probability and independent events(properties).
Reliability of systems. Random variable (types, distribution function).
Functional characteristics of discrete and continuous random variables.
Numerical characteristics of discrete and continuous random variables.
Basic discrete distributions A, Bi, H, Po (properties and use).
Basic continuous distributions R, N, E (properties and use).
Random vector, types, functional and numerical characteristics.
Distribution of transformed random variables.
Random sample, sample characteristics (properties, sample from N).
Parameter estimation (point and interval estimates of parameters Bi and N).
Testing statistical hypotheses.
Testing hypotheses of parameters of Bi and N.
Computer-assisted exercise
26 hours, compulsory
Syllabus
Descriptive statistics (one-dimensional sample with a quantitative variable). Software Statistica.
Descriptive statistics (two-dimensional sample with a quantitative variables). Combinatorics.
Probability (properties and calculating). Semester work assignment.
Conditioned probability. Independent events.
Written exam (3-4 examples). Functional and numerical characteristics of random variable.
Functional and numerical characteristics of random variable – achievement.
Probability distributions (Bi, H, Po, N), approximation.
Random vector, functional and numerical characteristics.
Point and interval estimates of parameters Bi and N.
Written exam (3-4 examples).
Testing hypotheses of parameters Bi and N.
Testing hypotheses of parameters Bi and N – achievement.
Tests of fit.