1. SylabUZ
2. Wydział Fizyki i Astronomii
3. semestr zimowy 2022/2023
4. Fizyka - pierwszego stopnia z tyt. licencjata
5. Probability and statistics

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Probability and statistics - opis przedmiotu

Cel przedmiotu

Acquaint students with the basics of the data analysis and statistical inference. Development of skills in application of the standard techniques used for data analysis and for simulations supporting this analysis with the use of the public domain software.

Wymagania wstępne

Zapisz zmiany

Metrology, first physics laboratory, knowledge of mathematical methods of physics, elements of the statistical analysis.

Zakres tematyczny

- Measurement uncertainty: significant digits and their rounding, the distribution of the population and the distribution of the sample, calculation of the mean, median, mode, standard deviation, range of variation and the average deviation.

- Probability distributions: calculation of the moments of a random variable with a known probability distribution, the cumulative distribution function and estimation of probabilities.

- Error Analysis: instrumental and statistical uncertainties, the equation of propagation of error, variance and covariance, the particular cases of error propagation, variance and covariance, computer implementations.

- Estimation of averages and errors: estimation of a mean, standard deviation and standard error, weighted estimates, relative estimates, testing of statistical hypothesis: Student's t-test and χ².

- Monte Carlo Techniques: random numbers generators, generation of random numbers from various probability distributions by the transformation of a homogeneous distribution, examples of simulations of simple measuring systems and experiments.

- Fitting to a stright line with the least squares method: linear regression exercises, solving normal equations and graphics science.

- Least squares method for polynominal fitting: solving of normal equations with determinant and matrix methods, fitting by using discrete orthogonal polynomials and Legendre polynomials.

- Least squares method: Marquardt'a-Levenberg method as the optimal method for linear and non-linear fit.

- Fit testing: χ² test, χ² distribution, correlation coefficient, multi-dimensional correlations,
F-test, confidence intervals, the Monte Carlo test.

- Grace - the program for presentation and analysis of data: data loading, operations on data, the graphic presentation, linear regression, curves fitting.

Metody kształcenia

Conventional lecture, probabilistic experiment.

Calculus exercises, programming exercises, computer simulations.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Lecture: written exam.

Classes: passing test, and performing the statistical project.

Final evaluation of laboratory exercises: arithmetic mean of the test and the project grades.

Final evaluation of the course: arithmetic mean of the exam and laboratory grades.

Literatura podstawowa

1. J.R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements 2nd Edition, University Science Books, 1996.

2. P.R. Bevington, D.K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, Third Edition, McGraw-Hill, 2003.

Literatura uzupełniająca

1. S. Brandt, Data Analysis: Statistical and Computational Methods for Scientists and Engineers, 3rd Edition,  Springer, 1998.

Uwagi

Zmodyfikowane przez dr Marcin Kośmider (ostatnia modyfikacja: 04-04-2022 20:51)