This Book is the second edition that intended to be textbook studied for undergraduate/ postgraduate course in mathematical statistics. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces events and probability review. Chapter Two devotes to random variables in their two types: discrete and continuous with definitions of probability mass function, probability density function and cumulative distribution function as well. Chapter Three discusses mathematical expectation with its special types such as: moments, moment generating function and other related topics. Chapter Four deals with some special discrete distributions: (Discrete Uniform, Bernoulli, Binomial, Poisson, Geometric, Negative Binomial and Hypergeometric) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Chapter Five deals with some special continuous distributions: (Uniform, Normal, Exponential, Gamma and Beta) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Many solved examples are intended in this book (obtaining mean and variance of distributions by m.g.f.). Chapter Six introduces univariate discrete and continuous transformations, i.e., one dimensional variables and their yielding probability distributions. Chapter Seven devotes to truncation of distributions from left, right or both sides, beside the probability distribution of order statistics. Chapter Eight discusses mathematical features of joint, marginal and conditional distributions, as well as independency via covariance and correlation of bivariate distributions. Chapter Nine deals with some special topics such as getting distribution for some transformation from multidimensional random variables by using moment generating function (m.g.f.) and cumulative distribution function (C.D.F.) Many solved examples (about 100) are intended in this book, in addition to a variety of unsolved relied problems (about 150) at the end of each chapter to enrich the statistical knowledge of our readers.
Total dissolved solids are at the top of the parameters list of water quality that requires investigations for planning and management, especially for irrigation and drinking purposes. If the quality of water is sufficiently predictable, then appropriate management is possible. In the current study, Multiple Linear Regression (MLR) and Artificial Neural Network (ANN) models were used as indicators of water quality and for the prediction of Total Dissolved Solids (TDS) along the Tigris River, in Baghdad city. To build these models five water parameters were selected from the intakes of four water treatment plants on the Tigris River, for the period between 2013 and 2017. The selected water parameters were Total Dissolved Solids (TDS
... Show MoreIn this paper, the wear in layers of articular cartilage was calculated, parameters effective on elastic deformation were studied in normal and diseased knee joints, and relations between elastic deformation and squeeze film characteristics under lubrication condition were discussed with using a mathematical model. Conferring to the results obtained, elastic deformation effects on the performance of synovial human knee joint were analyzed from medical and dynamics perspectives. Relationships between elastic deformation and wear of layers were also discussed.
Abstract\
In this research we built a mathematical model of the transportation problem for data of General Company for Grain Under the environment of variable demand ,and situations of incapableness to determining the supply required quantities as a result of economic and commercial reasons, also restrict flow of grain amounts was specified to a known level by the decision makers to ensure that the stock of reserves for emergency situations that face the company from decrease, or non-arrival of the amount of grain to silos , also it took the capabilities of the tanker into consideration and the grain have been restricted to avoid shortages and lack of processing capability, Function has been adopted
... Show MoreWater quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their performance is evaluated usin
... Show MoreWater quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their perfor
... Show MoreA mathematical method with a new algorithm with the aid of Matlab language is proposed to compute the linear equivalence (or the recursion length) of the pseudo-random key-stream periodic sequences using Fourier transform. The proposed method enables the computation of the linear equivalence to determine the degree of the complexity of any binary or real periodic sequences produced from linear or nonlinear key-stream generators. The procedure can be used with comparatively greater computational ease and efficiency. The results of this algorithm are compared with Berlekamp-Massey (BM) method and good results are obtained where the results of the Fourier transform are more accurate than those of (BM) method for computing the linear equivalenc
... Show MoreUse Almtafr Alcderan orange, one of the factors Hashr Alttafaria to study Alatjabh isolates elected on the basis of specifications so that was a positive response with mutagen record and system consisting of three isolates used Alcderan orange graded concentrations and under specific Trov similar conditions Alttafar Pal NTG compared
The objective of the research is to uncover the effect of the strategy of Quranic verses in the collection of science and systemic intelligence for second-grade students. The research sample consisted of (48) students of second grade students in the middle of Al Rasheed Boys School of the second Karkh Directorate, Distribution in the two divisions, Division of (b) and experimental group that studied strategy of Quranic verses, and the Division (a) control group which studied the regular way, and results indicated a statistically significant differences for the experimental group students studied using the strategy Verses in systemic intelligence collection.
The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ
Pollution of the aquatic environment and the depletion of the natural resource cause imbalance in the natural balance of the river environment and contributes to the deterioration of life and the killing of living organisms. Most of the old and modern cities and urban centers were set up close to the rivers because water enters the main lifeblood and all its facilities. The proximity of cities to rivers caused environmental problems resulting from the dumping of residues of these cities to a large and continuous, these wastes include all uses of the city (industrial, agricultural, residential and commercial) and others. The accumulation of these wastes inside the rivers water kills life and makes them unsuitable for various uses to bury
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