Mathematical Expectation, Variance and Covariance

1968 ◽  
pp. 229-238
Author(s):  
H. Mulholland ◽  
C. R. Jones
Keyword(s):  
Mathematical Expectation

COMBINATORIAL POLYNOMIALLY COMPUTABLE CHARACTERISTICS OF SUBSTITUTIONS AND THEIR PROPERTIES

2020 ◽  
Vol 7 (2) ◽  
pp. 34-41
Author(s):  
VLADIMIR NIKONOV ◽  
◽  
ANTON ZOBOV ◽  
Keyword(s):  
Mathematical Expectation ◽  
Point Of View ◽  
Small Range ◽  
Computational Point ◽  
Wide Range ◽  
Bijective Function ◽  
The Difference ◽  
Element Base ◽  
Selection Of

The construction and selection of a suitable bijective function, that is, substitution, is now becoming an important applied task, particularly for building block encryption systems. Many articles have suggested using different approaches to determining the quality of substitution, but most of them are highly computationally complex. The solution of this problem will significantly expand the range of methods for constructing and analyzing scheme in information protection systems. The purpose of research is to find easily measurable characteristics of substitutions, allowing to evaluate their quality, and also measures of the proximity of a particular substitutions to a random one, or its distance from it. For this purpose, several characteristics were proposed in this work: difference and polynomial, and their mathematical expectation was found, as well as variance for the difference characteristic. This allows us to make a conclusion about its quality by comparing the result of calculating the characteristic for a particular substitution with the calculated mathematical expectation. From a computational point of view, the thesises of the article are of exceptional interest due to the simplicity of the algorithm for quantifying the quality of bijective function substitutions. By its nature, the operation of calculating the difference characteristic carries out a simple summation of integer terms in a fixed and small range. Such an operation, both in the modern and in the prospective element base, is embedded in the logic of a wide range of functional elements, especially when implementing computational actions in the optical range, or on other carriers related to the field of nanotechnology.

scholarly journals On a non-homogeneous difference equation from probability theory

2009 ◽  
Vol 43 (1) ◽  
pp. 81-90 ◽  
Author(s):  
Jean-Luc Guilbault ◽  
Mario Lefebvre
Keyword(s):  
Probability Theory ◽  
Markov Chain ◽  
Difference Equation ◽  
Mathematical Expectation ◽  
Transition Probabilities ◽  
Current State ◽  
Constant Coefficients ◽  
Gambler’S Ruin ◽  
Gambler's Ruin Problem ◽  
Ruin Problem

Abstract The so-called gambler’s ruin problem in probability theory is considered for a Markov chain having transition probabilities depending on the current state. This problem leads to a non-homogeneous difference equation with non-constant coefficients for the expected duration of the game. This mathematical expectation is computed explicitly.

scholarly journals On Mathematical Statistics and its application to Political Economy and Insurance. (Continued from page 189.)

1873 ◽  
Vol 17 (5) ◽  
pp. 355-369
Author(s):  
Theodor Wittstein
Keyword(s):  
Political Economy ◽  
Mathematical Expectation ◽  
Probable Error ◽  
Mathematical Statistics ◽  
Most Probable Number ◽  
Probable Number ◽  
To Receive

Besides the probable error above considered, there is another quantity of some importance in practice, which may be called the Risk of a departure from the most probable number of survivers. It is obtained by adding together the products of all the possible positive deviations in the number of the survivers from its most probable value, each multiplied into the probability of its occurrence; or by adding together the products of all the possible negative deviations in the number of the survivers from its most probable value, each multiplied into the probability of its occurrence; in this case, however, taken without sign. For if we consider the deviations from the most probable number of survivers, taken without regard to sign, as represented by proportional sums of money, then the quantity just defined evidently expresses either the mathematical expectation of gain of a person who is to receive those sums, or the mathematical expectation of loss of a person who is to pay them. The latter of these two ideas more generally occurs in practice.

Estimation of Mathematical Expectation

2017 ◽  
pp. 351-440
Author(s):  
Vyacheslav Tuzlukov
Keyword(s):  
Mathematical Expectation

scholarly journals Reducing of noise structure influence on an accuracy of a desired signal extraction

2018 ◽  
Vol 15 (3) ◽  
pp. 365-370 ◽  
Author(s):  
Vladimir Marchuk
Keyword(s):  
Signal Processing ◽  
Mathematical Expectation ◽  
Random Processes ◽  
Parameters Estimation ◽  
Signal Extraction ◽  
Scientific Contribution ◽  
Noise Component ◽  
Component Structure ◽  
Noise Structure ◽  
Theoretical Results

In the paper, the issues regarding the analysis of the noise component structure are addressed and methods for reducing the error in estimating of the mathematical expectation of the noise component are proposed. The use of the proposed method of ?noise purification? makes possibility to reduce the error introduced by the noise structure when estimating the mathematical expectation and dispersion of the noise component during research. The main scientific contribution in this paper in accuracy increasing of random processes parameters estimation. These theoretical results can be applied in different spheres of data analyzing and signal processing when random processes have some structure.

scholarly journals Analytical Relations for the Mathematical Expectation and Variance of a Standard Distributed Random Variable Subjected to the √X Transformation

2018 ◽  
Vol 63 (3) ◽  
pp. 215 ◽  
Author(s):  
P. Kosobutsky
Keyword(s):  
Distribution Function ◽  
Mathematical Expectation ◽  
Random Variable ◽  
Standard Distribution ◽  
Physical Variables ◽  
Analytical Relations

The mathematical expectation and the variance have been calculated for random physical variables with the standard distribution function that are transformed by functionally related direct quadratic, X2, and inverse quadratic, √X, dependences.

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