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.
Background: Urolithiasis and hypertension are prevalent and clinically significant conditions in the Middle East, both influenced by shared metabolic and environmental risk factors. Understanding the potential association between them is important for guiding prevention strategies. Objective: To explore the relationship between urolithiasis and hypertension in a sample of Iraqi adult patients. Methods: A cross-sectional observational study was conducted at Alkindy Teaching Hospital, Baghdad, from September 2024 to March 2025. Participants included 237 patients with confirmed urinary tract stones and 244 controls confirmed to be stone-free, matched for age and sex. Exclusion criteria included secondary hypertension, chronic kidney di
... Show MoreObesity is a worldwide health complication. In 2014, 600 million adults and 42 million kids, less than five years of age, were obese. It is a hyperassembly of energy in the form of adipose tissues which has worse effects on health. The major factors of the obesity epidemic are: heavy meal which is rich in lipids, carbohydrates resulting in overweight and eventually obesity, and a decrease in physical activity that leads to defects in calorie conception. In health care facilities ferritin assay is used as a screening test to detect iron deficiency; however, its reliability in obesity has been questioned. The present study aimed to assess and compare the incidence of obesity, hyperferritinemia, hyperlipidemia, and hypouricemia among middle-ag
... Show More
The objective of this study was to develop neural network algorithm, (Multilayer Perceptron), based correlations for the prediction overall volumetric mass-transfer coefficient (kLa), in slurry bubble column for gas-liquid-solid systems. The Multilayer Perceptron is a novel technique based on the feature generation approach using back propagation neural network. Measurements of overall volumetric mass transfer coefficient were made with the air - Water, air - Glycerin and air - Alcohol systems as the liquid phase in bubble column of 0.15 m diameter. For operation with gas velocity in the range 0-20 cm/sec, the overall volumetric mass transfer coefficient was found to decrease w
... Show MoreNew series of metal ions complexes have been prepared from the new ligand [4-Amino-N-(5-methyl-isaxazol-3-yl)-benzenesulfonamide] derived from Sulfamethoxazole and 3-aminophenol. Accordingly, mono-nuclear Mn(II), Fe(III), Co (II), and Rh(III) complexes were prepared by the reaction of previous ligand with MnCl2.4H2O, CoCl2.6H2O, FeCl3.6H2O and RhCl3H2O, respectively. The compounds have been characterized by Fourier-transform infrared (FTIR), ultraviolet–visible (UV–vis), mass, 1H-, and 13C-nuclear magnetic resonance (NMR) spectra and thermo gravimetric analysis (TGA& DSC) curve, Bohr magnetic (B.M.), elemental microanal
... Show More4-Amino-N-(5-methyl-isaxazol-3-yl)-benzenesulfonamide, a new azo (LH) ligand, was synthesized by reacting the diazonium salt of Sulfamethoxazole with coupling compound 3-amino phenol. Spectroscopic techniques (UV-Vis, FTIR, 1H &13C-NMR, and LC-Mass) as well as micro elemental analyses (C.H.N.O) and TGA and SDC were used to identify the azo ligand. Complexes of (Zn(II), Cr(III), Cu(II) and VO(II)) were produced and characterized by atomic absorption, elemental microanalysis, infrared, LC-Mass, TGA, DSC and UV-Vis spectral techniques, as well as conductivity and magnetic quantifications. All the complexes had a 1:2 metal-ligand ratio, and non-electrolytes at all complexes and tetrahedral geometry suggested except Cr-complex, which demonstrate
... Show MoreThis paper presents a new azo dye 3-[2-(1H-indol-2-yl)ethyldiazenyl]quinolin-2-ol] from the reaction of the diazonium salt derived from tryptamine and 2-hydroxyquinoline. Azo dye was used to prepare a series of complexes with the chlorides of Ni(II), Pt(IV), Pd(II), Cd(II), and Zn(II). Compounds were analyzed and characterized using elemental analysis, magnetic measurement, UV-vis, IR, MS, NMR, and conductivity. The findings demonstrated that the ligand acts as ionic in complex form, O-bidentate, supporting the proposed formula. The complexes generally exhibited tetrahedral and octahedral geometries, except the palladium complex, which adopted a square planar geometry. TGA was used to investigate the thermal characteristics of compo
... Show MoreNew series of metal ions complexes have been prepared from the new ligand [4-Amino-N-(5- methyl-isaxazol-3-yl)-benzenesulfonamide] derived from Sulfamethoxazole and 3-aminophenol. Accordingly, mono-nuclear Mn(II), Fe(III), Co (II), and Rh(III) complexes were prepared by the reaction of previous ligand with MnCl2.4H2O, CoCl2.6H2O, FeCl3.6H2O and RhCl3H2O, respectively. The compounds have been characterized by Fourier-transform infrared (FTIR), ultraviolet–visible (UV–vis), mass, 1H-, and 13C-nuclear magnetic resonance (NMR) spectra and thermo gravimetric analysis (TGA& DSC) curve, Bohr magnetic (B.M.), elemental microanalyses, metal ions, chloride containing, and molar conductance.These reviews uncovered octahedral geometries for complex
... Show MoreMass transfer was examined at a stationary rectangular copper electrode (cathode) by using the reduction of cupric ions as the electrochemical reaction. The influence of electrolyte temperature (25, 45, and 65 oC), and cupric ions concentration (4, 8, and 12 mM) on mass transfer coefficient were investigated by using limiting current technique. The mass transfer coefficient and hence the Sherwood number was correlated as Sh =
The 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 with octahed
... Show MoreBackground: Endometriosis is defined as the presence or growth of ectopic endometrial tissue outside their usual site ( the uterus). It is a common condition in women. It may occur in the ovaries, fallopian tubes, vagina and rarely, endometriosis may occur in the abdomen and lungs. Endometriosis is common among women of reproductive age. It is either primary or secondary. The triad of diagnosis is a pain with menstruation, cesarean scar and a mass in the scar.
... Show More