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Probability and Statistics by Example, Vol. 1
Vol. 1: Basic Probability and Statistics.
Cambridge :
Cambridge University Press, 2014.
Kelbert M., Suhov Y.
Probability and statistics are as much about intuition and problem solving as they are about theorem proving. Consequently,
students can find it difficult to make a successful transition from lectures, to examinations, to practice because the problems
involved can vary so much in nature. Since the subject is critical in so many applications, from insurance, to telecommunications,
to bioinformatics, the authors have collected more than 200 worked examples to help the students develop a deep
understanding of the subject rather than a superficial knowledge of sophisticated theories. With amusing stories and
historical asides sprinkled thoughout, this enjoyable book will leave students better equipped to solve problems in practice
and under exam conditions.
Keywords: теория вероятностейматематическая статистикаprobabilityтеория вероятностей и математическая статистикаmathematical statistics
Publication based on the results of:
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Sergei L. Semakov, , in: Proceedings of the 2026 12th International Conference on Control, Decision and Information Technologies (CoDIT) (Italy, Bari, July 13–16, 2026).: IEEE, 2026. P. 153–156.
The problem of the first achievement of a given level by a random process is considered. The previously obtained general results are specified for a smooth Gaussian process. ...
Added: August 24, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Semenov P., Математика в школе 2024 № 4 С. 34–40
Simple examples are given to show that
the independence of two random events is a very
rare circumstance. It is shown how to estimate its
frequency. Open questions are posed ...
Added: March 14, 2026
Семаков С. Л., Автоматика и телемеханика 2025 № 12 С. 104–118
This paper considers the problem of estimating the probability of the following event: a continuous random process will first reach a given level at some time from a given variation interval of the independent variable. The general results obtained previously are specified for a smooth Gaussian process. The estimates are calculated for different values of ...
Added: February 23, 2026
Dvoinin A., Информация и образование: границы коммуникаций 2025 Т. 25 № 17 С. 125–127
The article discusses problems of applying statistical methods in pedagogical research: the lack of informative indicators, template types of analysis, fabrication of calculations, p-hacking and others. ...
Added: August 19, 2025
Semakov S., Semakov A., Semakov I., , in: 62nd IEEE Conference on Decision and Control (CDC), Singapore, Singapore, 2023.: IEEE, 2023. P. 3820–3825.
We estimate the probability that the first achievement of a given level by the component y_1(x) of n-dimensional continuous process y(x)={y_1(x),…,y_n(x)} occurs at some moment x* from a given interval (x′,x′′) and, at this moment x*, the condition (y_2(x*),…,y_n(x*))∈D holds, where D is a given domain of (n−1)-dimensional Euclidean space R^(n−1). The need to calculate the abovementioned probability arises in the problems of aircraft control during landing. ...
Added: August 9, 2025
Sergei L. Semakov, IEEE Transactions on Information Theory 2024 Vol. 70 No. 10 P. 7162–7178
We propose a scheme for finding the probabilities of events related to crossings of a level by a random process. Using this scheme, we estimate the probability that the first achievement of a given level by the component y_1(x) of an n-dimensional continuous process y(x)={y_1(x),…,y_n(x)} occurs at some moment x* from a given interval (x′,x′′) and, at this moment x* , the other components y_2(x*),…,y_n(x*) satisfy given ...
Added: August 3, 2025
Sergei Semakov, International Journal of Dynamics and Control 2025 Vol. 13 No. 5 Article 201
We consider the problem of the exit of a diffusion Markov process to the boundary of a given domain. We concentrate on the one-dimensional case and solve the problem of finding the probability that the first exit of the process beyond the established corridor will occur at a given time. We apply the obtained results ...
Added: August 2, 2025
Булинский А. В., Трещев Д. В., Яровая Е. Б., Успехи математических наук 2025 Т. 80 № 1(481) С. 171–177
Описываются научные достижения выдающегося математика академика РАН А.Н.Ширяева. ...
Added: June 26, 2025