Probability theory and mathematical statistics

2021 ◽  
Author(s):  
Irina Paliy
Keyword(s):  
Probability Theory ◽  
Queuing Theory ◽  
Interval Estimation ◽  
Random Variables ◽  
Mathematical Statistics ◽  
Estimation Of Parameters ◽  
Introductory Course ◽  
Fields Of Study ◽  
Discrete Random Variables ◽  
Statistical Hypotheses

The tutorial is an introductory course in probability theory and mathematical statistics. Elements of combinatorics, basic concepts and theorems of probability theory, discrete random variables, continuous random variables, some limit theorems, one-dimensional and two-dimensional samples, point and interval estimation of parameters of the general population, testing of statistical hypotheses, elements of queuing theory are considered. The presentation of the theoretical material is accompanied by a large number of detailed examples of problem solving. For students of technical and economic fields of study and specialties, studying under the bachelor's and specialty programs.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

scholarly journals The number of failed components in a coherent working system when the lifetimes are discretely distributed

Metrika ◽  
2021 ◽  
Author(s):  
Krzysztof Jasiński
Keyword(s):  
Random Variables ◽  
Continuous Case ◽  
Coherent System ◽  
Coherent Systems ◽  
Discrete Random Variables ◽  
Independent And Identically Distributed

AbstractIn this paper, we study the number of failed components of a coherent system. We consider the case when the component lifetimes are discrete random variables that may be dependent and non-identically distributed. Firstly, we compute the probability that there are exactly i, $$i=0,\ldots ,n-k,$$ i = 0 , … , n - k , failures in a k-out-of-n system under the condition that it is operating at time t. Next, we extend this result to other coherent systems. In addition, we show that, in the most popular model of independent and identically distributed component lifetimes, the obtained probability corresponds to the respective one derived in the continuous case and existing in the literature.

Stochastic hydrology-how much hydrology does it contain and how much does it matter?

1984 ◽  
Vol 16 (1) ◽  
pp. 19-19
Author(s):  
V. Klemeš
Keyword(s):  
Water Management ◽  
Probability Theory ◽  
Stochastic Models ◽  
Mathematical Statistics ◽  
Stochastic Hydrology ◽  
Management Decisions ◽  
Quality Of Water ◽  
The Way

Most of what is routinely labeled ‘stochastic hydrology’ does not contain any hydrology at all and could be more properly identified as the fitting of stochastic models to samples of data of hydrologic origin. T0 engage in this enterprise, no hydrologic knowledge is necessary, nor do the results contribute to hydrologic knowledge. Moreover, the bulk of the current stochastic hydrology does not appreciably enhance the quality of water management decisions-an aim which provided the original impetus for its development. It seems that the mainstream of stochastic hydrology follows in the steps of ‘dam theory’, the only difference being that while the latter has become a self-contained branch of pure probability theory, the former is on the way to becoming a branch of pure mathematical statistics.

Two-stage stochastic programming problems involving interval discrete random variables

OPSEARCH ◽  
2012 ◽  
Vol 49 (3) ◽  
pp. 280-298 ◽  
Author(s):  
Suresh Kumar Barik ◽  
Mahendra Prasad Biswal ◽  
Debashish Chakravarty
Keyword(s):  
Stochastic Programming ◽  
Random Variables ◽  
Two Stage ◽  
Discrete Random Variables

Specifications of Machine-Tool Equipment: Forecasting Techniques

2015 ◽  
Vol 788 ◽  
pp. 318-324
Author(s):  
Egor A. Zverev ◽  
Pavel Tregubchak ◽  
Nikita Vakhrushev ◽  
Stanislav Ptitsyn
Keyword(s):  
Probability Theory ◽  
Machine Tool ◽  
Machine Tools ◽  
Automated Design ◽  
General Concept ◽  
Mathematical Statistics ◽  
Development Phase ◽  
Design Engineering ◽  
Engineering Systems ◽  
Initial Development

The problems of theoretical grounds of machine tools specifications based on mathematic operational simulation are discussed in the paper. The proposed approach is based on the probability theory and mathematical statistics apparatus. It is universal and makes it possible to use automated design engineering systems at an initial development phase of the general concept of new equipment.

ANALYSIS OF FUZZY QUEUES BY USING PENTAGONAL FUZZY NUMBER

2021 ◽  
Vol 23 (04) ◽  
pp. 211-224
Author(s):  
Gurcharan Singh ◽  
◽  
Baljodh Singh ◽  
Neelam Kumari ◽  
◽  
...  
Keyword(s):  
Probability Theory ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Queuing Theory ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Linguistic Terms

This paper deals with the fact thatpentagonal fuzzy numbers are pre-owned and systematic outcomes are discussed in real-life situations. The fuzzy set supposition is combined with well-established classical queuing theory but the classical queuing theory is far away from real-life situations. In this approach, we can use both fuzzy and probability theory to make this work more realistic with the help of the α-cut technique. Symmetric pentagonal fuzzy numbers are used to elaborate on the situation of the queue in linguistic terms.

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