Module also offered within study programmes:
General information:
Name:
Probability and Statistics
Course of study:
2017/2018
Code:
IES-1-202-s
Faculty of:
Computer Science, Electronics and Telecommunications
Study level:
First-cycle studies
Specialty:
-
Field of study:
Electronics and Telecommunications
Semester:
2
Profile of education:
Academic (A)
Lecture language:
English
Form and type of study:
Full-time studies
Course homepage:
 
Responsible teacher:
prof. dr hab. inż. Zakrzewska Katarzyna (zak@agh.edu.pl)
Academic teachers:
dr inż. Swatowska Barbara (swatow@agh.edu.pl)
prof. dr hab. inż. Zakrzewska Katarzyna (zak@agh.edu.pl)
Module summary

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Social competence
M_K001 He knows that an appropriate probabilistic and statistical analysis can help to understand the importance of the accuracy of the device and its measurement possibilities. ES1A_K01, ES1A_K02 Test
Skills
M_U001 He can solve tasks using terms of combinatorics. ES1A_U02, ES1A_U01 Examination
M_U002 Can calculate the total, conditional and independent probability in relation to specific examples. ES1A_U07 Examination
M_U003 He can use the known methods and mathematical models and computer simulations to analyze the experimental data, indicating the confidence intervals and the accuracy of the result. ES1A_U02, ES1A_U01 Examination
Knowledge
M_W001 Has knowledge of the terms of combinatorics ES1A_W01 Examination
M_W002 Has knowledge of the probabilistic description. ES1A_W01, ES1A_W14 Examination
M_W003 He has ordered and well-established knowledge of statistical analysis of experimental data. ES1A_W01, ES1A_W06 Examination
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Others
E-learning
Social competence
M_K001 He knows that an appropriate probabilistic and statistical analysis can help to understand the importance of the accuracy of the device and its measurement possibilities. + + - - - - - - - - -
Skills
M_U001 He can solve tasks using terms of combinatorics. + + - - - - - - - - -
M_U002 Can calculate the total, conditional and independent probability in relation to specific examples. + + - - - - - - - - -
M_U003 He can use the known methods and mathematical models and computer simulations to analyze the experimental data, indicating the confidence intervals and the accuracy of the result. + + - - - - - - - - -
Knowledge
M_W001 Has knowledge of the terms of combinatorics + + - - - - - - - - -
M_W002 Has knowledge of the probabilistic description. + + - - - - - - - - -
M_W003 He has ordered and well-established knowledge of statistical analysis of experimental data. + + - - - - - - - - -
Module content
Lectures:

Classes within the module are carried out in the form of lectures (30 hours) and
computational exercises (15 hours)

Lectures

1. Introduction (2h)
Historical background; the concept of probability; the paradox of the Chevalier de Méré; the role of probability and statistics in science and engineering; type of statistical data and their graphical representation.
2. Probability (4h)
Sample spaces and events; definitions and interpretation of probability, elements of combinatorics (permutations, combinations), conditional probability; independence; Bayes’ theorem; random variables; advanced problems concerning probability.
3. Discrete random variables and probability distributions (4h)
Probability mass function; cumulative distribution function; mean and variance of a discrete random variable; quantiles, median, mode, range, discrete uniform distribution; binomial distribution; hypergeometric distribution; Poisson distribution.
4. Continuous random variables and probability distributions (4h)
Probability density function; normal distribution; exponential distribution; Erlang and Gamma distribution; Weibull distribution; Lognormal distribution; calculations of mean and variance of distributions of continuous random variables; examples of integration.
5. Joint probability distribution (4h)
Two independent variables, linear combinations of random variables, covariance and correlation, simple linear regression, non-linear regression.
6. Estimation of parameters (2h)
General concept of point estimation, population and sampling, losowanie, estimators: consistent, unbiased, efficient, point estimation, statistical intervals for a single sample, confidence intervals, level of confidence.
7. Statistical inference (4h)
Types and verification of hypotheses, parametric tests of significance; errors of type I and II.
8. Application of statistical methods (6h)
Uncertainty in the experimental measurements; statistical physics, quantum mechanical statistics (Fermi-Dirac, Bose-Einsteina).

Auditorium classes:

Tutorials

1. Combinatorics, the Newton’s symbol (2h).
2. Probability: total, conditional and independent; Bayes Theorem (2h).
3. Random variable and cumulative distribution (2h).
4. Calculating the probability by using density (2h).
5. Introduction to Statistics: average, standard deviation, variance (2h).
6. Regression analysis of the sample data (2h).
7. Calculation of confidence intervals for the different data (2h).
8. Verification what has been learned – final test (1h).

Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 77 h
Module ECTS credits 3 ECTS
Participation in lectures 28 h
Participation in auditorium classes 14 h
Realization of independently performed tasks 15 h
Preparation of a report, presentation, written work, etc. 20 h
Additional information
Method of calculating the final grade:

1. Warunkiem koniecznym uzyskania pozytywnej oceny końcowej OK. jest otrzymanie pozytywnej oceny
z laboratorium i z egzaminu. Przy czym warunkiem dopuszczenia do egzaminu jest posiadanie oceny pozytywnej z laboratorium.
2. Po obliczeniu oceny średniej ważonej według wzoru SW = 0,4SOL+0,6SOE, gdzie SOL jest średnią arytmetyczną ocen uzyskanych we wszystkich terminach z laboratorium, a SOE jest średnią arytmetyczną ocen uzyskanych we wszystkich terminach z egzaminu, ocena końcowa OK jest obliczana według zależności:
if SW >4.75 then OK:=5.0 (bdb) else
if SW >4.25 then OK:=4.5 (db) else
if SW >3.75 then OK:=4.0 (db) else
if SW >3.25 then OK:=3.5 (dst) else OK:=3 (dst)

Prerequisites and additional requirements:

Znajomość algebry i analizy wektorów.

Recommended literature and teaching resources:

1. Douglas C. Montgomery, George C. Runger, “Applied Statistics and Probability for Engineers”, Third Edition, John Wiley & Sons, 2003
2. Sobczyk M., “Statystyka”, Wydawnictwo Naukowe PWN, Warszawa, 1996

Scientific publications of module course instructors related to the topic of the module:

Additional scientific publications not specified

Additional information:

None