Pasha Zusmanovich - teaching

A.T. Fomenko, Geometry and Probability,
Ink and pencil on paper, 38 x 47.5 cm, 1987

6PAS2 Probability and Statistic 2,
summer semester 2025/2026

APPROXIMATE SYLLABUS

The subject of statistics. Types of data.
Basic notions of descriptive statistics: mean, median, mode, quantiles, standard deviation.
Correlation, correlation matrices.
Normal distribution. Confidence interval.
Various types of distributions.
Null and alternative hypotheses. Hypothesis testing.
Statistical models. Linear regression. Least squares.
Clustering.
Working with R.

A parallel Czech-English text covering some of the topics in probablity and statistics is available on the page of Probability & Statistics 1.

LITERATURE

J. Albert and M. Rizzo, R by Example, Springer, 2012.
C.-H. Chen, Generalized association plots: information visualization via iterative generated correlation matrices, Statistica Sinica 12 (2002), 7-29.
Y. Cohen and J.Y. Cohen, Statistics and Data with R, Wiley, 2008.
M.J. Crawley, Statistics: An Introduction Using R, 2nd ed., Wiley, 2014. (1st edition)
M.J. Crawley, The R Book, 2nd ed., Wiley, 2013.
P. Dalgaard, Introductory Statistics with R, 2nd ed., Springer, 2008.
B.S. Everitt and T. Hothorn, A Handbook of Statistical Analyses Using R, 2nd ed., Chapman & Hall/CRC, 2010. (1st edition)
L. Gonick and W. Smith, The Cartoon Guide to Statistics, HarperPerennial, 1993.
Handbook of Statistics. Volume 32. Computational Statistics with R (ed. M.B. Rao and C.R. Rao), Elsevier, 2014.
J. Maindonald and W.J. Braun, Data Analysis and Graphics Using R, 3rd ed., Cambridge Univ. Press, 2010. (2nd edition)
L. Pace, Beginning R. An Introduction to Statistical Programming, Apress, 2012.
R. Pruim, Foundations and Applications of Statistics. An Introduction Using R, 2nd ed., AMS, 2018.
W.N. Venables, D.M. Smith et al., An Introduction to R, 2015. (old edition)
J. Verzani, Using R for Introductory Statistics, 2nd ed., Chapman & Hall/CRC, 2014. (1st edition)

All the books are available in electronic form in multiple places.

= available in the university library

SOFTWARE: R
Online sources:

R Programming, Wikibook.
Stack Exchange sites: stackoverflow and Cross Validated.

A BRIEF SYNOPSIS

Class 1 February 11, 2026 (~1.5h)
Organizational issues. R.

Class 2 February 18, 2026 (~2h)
Discussion of homeworks 1-2. Mode . Skewness and kurtosis. Meaning and importance of the central limit theorem.
R code

Class 3 February 25, 2026 (~2h)
Discussion of homeworks 3-4. "Paradoxes" in statistics (according to T. Tao, Compactness and Contradiction, AMS 2013, Section 6.5). Weighted mean. Population weighted density. Simpson's paradox.
R code

Class 4 March 4, 2026 (~2.5h)
Discussion of homeworks 5-6. Central limit theorem (recap, according to Crawley, The R book, p.278). Why in the nonbiased estimator of the standard deviation we have \(n-1\) in the denominator, and not \(n\). Confidence interval (according to Dalgaard, pp.63-64). Tests for normality: normal scores, Q-Q plots (according to Cohen-Cohen, pp.220-223).
R code

Class 5 March 11, 2026 (~3h)
Discussion of homeworks 7-9. Correlation, correlation matrices. Iterated correlation matrices (according to Chen).

Class 6 March 18, 2026 (~2.5h)
Discussion of homeworks 10-12. Statistical models. Linear regression. Least squares. Residuals. (According to Albert and Rizzo, Chapter 7).

Class 7 March 25, 2026 (~3h)
Discussion of homeworks 10-14.

Class 8 April 1, 2026 (~3h)
Discussion of homeworks 12,14-16. Generalized additive models (after Crawley, Statistics: An Introduction Using R, pp.146-148).
R code

Class 9 April 8, 2026 (~1.5h)
Discussion of homeworks 17-18. Clustering (hierarchical, K-means, gravitational).

Class 10 April 15, 2026 (~2.5h)
Discussion of homeworks 15-20. Null and alternative hypotheses, p-values.

Class 11 April 29, 2026
Discussion of homeworks 21-23.

HOMEWORKS

Old material from "VAPMS Selected Applications of Mathematical Statistics", summer semester 2018/2019
A brief synopsys:

Homeworks

Created: Wed Sep 23 2015
Last modified: Wed May 6 2026 15:08:54 CEST

6PAS2 Probability and Statistic 2, summer semester 2025/2026

6PAS2 Probability and Statistic 2,
summer semester 2025/2026