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.
To detect the amount of Rifampicin in bulk and medicinal dosage formulations, an accurate, and cost-effective UV spectrophotometric technique has been developed using the area under the peak to estimate the presence of Rifampicin. This range of wavelengths (300–356) nm was chosen. The method showed linearity in the 2-22 μg/mL range, with R2 being 0.9996. The developed method' linearity, detection limit, quantification limit, precision, repeatability, and accuracy were all statistically and experimentally validated. The suggested methodology can be used for routine quality control analysis of Rifampicin in pure form and in capsule dosage form, as demonstrated by the satisfactory recovery percentage results. This study explores the struct
... Show MoreIn this paper we generalize some of the results due to Bell and Mason on a near-ring N admitting a derivation D , and we will show that the body of evidence on prime near-rings with derivations have the behavior of the ring. Our purpose in this work is to explore further this ring like behavior. Also, we show that under appropriate additional hypothesis a near-ring must be a commutative ring.
This paper develops a fuzzy multi-objective model for solving aggregate production planning problems that contain multiple products and multiple periods in uncertain environments. We seek to minimize total production cost and total labor cost. We adopted a new method that utilizes a Zimmermans approach to determine the tolerance and aspiration levels. The actual performance of an industrial company was used to prove the feasibility of the proposed model. The proposed model shows that the method is useful, generalizable, and can be applied to APP problems with other parameters.
The cathodic deposition of zinc from simulated chloride wastewater was used to characterize the mass transport properties of a flow-by fixed bed electrochemical reactor composed of vertical stack of stainless steel nets, operated in batch-recycle mode. The electrochemical reactor employed potential value in such a way that the zinc reduction occurred under mass transport control. This potential was determined by hydrodynamic voltammetry using a borate/chloride solution as supporting electrolyte on stainless steel rotating disc electrode. The results indicate that mass transfer coefficient (Km) increases with increasing of flow rate (Q) where .The electrochemical reactor proved to be efficient in removing zinc and was abl
... Show MoreBackground: Hair loss is a common distressing disease and challenging problem for many dermatologist. Telogen effluvium is the most common hair loss disease in which nutritional deficiencies may precipitate the disease through their effect on hair structure and growth.
Study Aim : Validating role of serum ferritin level and body mass index in Chronic Telogen Effluvium and analyzing association between these factors with socioeconomic, demographic, gynecological factors and weight loss effect. Establishing a nutritional preventive advice to improve treatment successfulness and decrease the disease occurrence.
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The heat and mass transfer coefficients of the indirect contact closed circuit cooling tower, ICCCCT, were investigated experimentally. Different experiments were conducted involving the controlling parameters such as air velocity, spray water to air mass flow rate ratio, spray water flow rate, ambient air wet bulb temperature and the provided heat load to investigate their effects on the performance of the ICCCCT. Also the effect of using packing on the performance of the ICCCCT was investigated. It was noticed that these parameters affect the tower performance and the use of packing materials is a good approach to enhance the performance for different operational conditions. Correlations for mass and heat transfer coefficients are pres
... Show MoreBackground: Diabetes mellitus a major factor that has adverse effects on the vascular system and the heart. It causes an increase in cardiac muscle thickness, resulting in decreased compliance and increased peripheral arterial stiffness. This study aims to assess the left ventricular mass (LVM) and left ventricular hemodynamic changes in diabetic patients measured by Doppler echocardiography. Patients and Methods: The study included 50 diabetic patients ranging in age between 25 and 80 years, (mean age: 54.1 ± 15.10, 19 males, 31 females) and 50 healthy subjects, aged 25 to 80 years (mean age: 48.52 ± 14.45, 11 males, 39 females). Doppler echocardiography was used to assess left ventricular function. The measurements included
... Show MoreThis study deals with knowing the types of research in public relations studies at the Faculty of Mass Communication for the period from 1989 to 2007 and knowing the methods that researchers used in their studies, as well as knowing the methods and tools of scientific research that were used, and whether one method or tool is used more than others, and knowing Samples used in the analysis. As well as the contents and types of this research The institutions that were subjected to the study, and the preparation of the respondents This research aims to answer the following questions:. A- What are the types of research and methods that were used in university theses that dealt with the topic? Public Relations at the Faculty of Media from 1989
... Show MoreThe researchers wanted to make a new azo imidazole as a follow-up to their previous work. The ligand 4-[(2-Amino-4-phenylazo)-methyl]-cyclohexane carboxylic acid as a derivative of trans-4-(aminomethyl) cyclohexane carboxylic acid diazonium salt, and synthesis a series of its chelate complexes with metalions, characterized these compounds using a variety technique, including elemental analysis, FTIR, LC-Mass, 1H-NMRand UV-Vis spectral process as well TGA, conductivity and magnetic quantifications. Analytical data showed that the Co (II) complex out to 1:1 metal-ligand ratio with square planner and tetrahedral geometry, respectively while 1:2 metal-ligand ratio in the Cu(II), Cr(III), Mn(II), Zn(II), Ru(III)and Rh(III)complexes
... Show MoreA novel metal complexes Cu (II), Co (II), Cd (II), Ru (III) from azo ligand 5-((2-(1H-indol-2-yl)
ethyl) diazinyl)-2-aminophenol were synthesized by simple substitution of tryptamine with 2-aminophenol.
Structures of all the newly synthesized compounds were characterized by FT IR, UV-Vis, Mass spectroscopy
and elemental analysis. In addition measurements of magnetic moments, molar conductance and atomic
absorption. Then study their thermal stability by using TGA and DSC curves. The DCS curve was used to
calculate the thermodynamic parameters ΔH, ΔS and Δ G. Analytical information showed that all complexes
achieve a metal:ligand ratio of [1:1]. In all complex examinations, the Ligand performs as a tri