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.
The nuclear ground-state structure of some Nickel (58-66Ni) isotopes has been investigated within the framework of the mean field approach using the self-consist Hartree-Fock calculations (HF) including the effective interactions of Skyrme. The Skyrme parameterizations SKM, SKM*, SI, SIII, SKO, SKE, SLY4, SKxs15, SKxs20 and SKxs25 have been utilized with HF method to study the nuclear ground state charge, mass, neutron and proton densities with the corresponding root mean square radii, charge form factors, binding energies and neutron skin thickness. The deduced results led to specifying one set or more of Skyrme parameterizations that used to achieve the best agreement with the available experimental
... Show MoreThe present work investigates the effect of; superficial air velocities of: 1, 3, and 6 cm/s for two types of perforated distributor on hydrodynamic characteristic in a gas-liquid dispersion column of; air-water, and airaqueous-n-propanol solution. Bubble distribution, gas holdup, and power consumption are parameters take in consideration. Experimental work was carried out in perspex column of 8.5 cm inside diameter and 1.5 m height. Two types of bubble generator (perforated plate) were fixed at the bottom of the column; plate A (99 holes of 0.5 mm diameter and free area of 0.34%), plate B (20 holes of 1.5 mm diameter and free area of 0.62%). Photographic technique was used to measure the bubble parameters. The experimental results were
... Show MoreDifferent frequency distributions models were fitted to the monthly data of raw water Turbidity at water treatment plants (WTPs) along Tigris River in Baghdad. Eight water treatment plants in Baghdad were selected, with raw water turbidity data for the period (2008-2014). The frequency distribution models used in this study are the Normal, Log-normal, Weibull, Exponential and two parameters Gamma type. The Kolmogorov-Smirnov test was used to evaluate the goodness of fit. The data for years (2008-2011) were used for building the models. The best fitted distributions were Log-Normal (LN) for Al-Karkh, Al-Wathbah, Al-Qadisiya, Al-Dawrah and, Al-Rashid WTPs. Gamma distribution fitted well for East Tigris and Al-Karamah
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Lightweight materials is used in the sheet metal hydroforming process, because it can be adapted to the manufacturing of complex structural components into a single body with high structural stiffness. Sheet hydroforming has been successfully developed in industry such as in the manufacturing of the components of automotive.The aim of this study is to simulate the experimental results ( such as the amount of pressure required to hydroforming process, stresses, and strains distribution) with results of finite element analyses (FEA) (ANSYS 11) for aluminum alloy (AA5652) sheets with thickness (1.2mm) before heat treatm
... Show MoreDifferent frequency distributions models were fitted to the monthly data of raw water Turbidity at water treatment plants (WTPs) along Tigris River in Baghdad. Eight water treatment plants in Baghdad were selected, with raw water turbidity data for the period (2008-2014). The frequency distribution models used in this study are the Normal, Log-normal, Weibull, Exponential and two parameters Gamma type. The Kolmogorov-Smirnov test was used to evaluate the goodness of fit. The data for years (2008-2011) were used for building the models. The best fitted distributions were Log-Normal (LN) for Al-Karkh, Al-Wathbah, Al-Qadisiya, Al- Dawrah and, Al-Rashid WTPs. Gamma distribution fitted well for East Tigris and Al-Karamah WTPs. As for Al-
... Show MoreThis thesis was aimed to study gas hydrates in terms of their equilibrium conditions in bulk and their effects on sedimentary rocks. The hydrate equilibrium measurements for different gas mixtures containing CH4, CO2 and N2 were determined experimentally using the PVT sapphire cell equipment. We imaged CO2 hydrate distribution in sandstone, and investigated the hydrate morphology and cluster characteristics via μCT. Moreover, the effect of hydrate formation on the P-wave velocities of sandstone was investigated experimentally.
The article describes a certain computation method of -arcs to construct the number of distinct -arcs in for . In this method, a new approach employed to compute the number of -arcs and the number of distinct arcs respectively. This approach is based on choosing the number of inequivalent classes } of -secant distributions that is the number of 4-secant, 3-secant, 2-secant, 1-secant and 0-secant in each process. The maximum size of -arc that has been constructed by this method is . The new method is a new tool to deal with the programming difficulties that sometimes may lead to programming problems represented by the increasing number of arcs. It is essential to reduce the established number of -arcs in each cons
... Show MoreDiabetic nephropathy (DN) is the foremost cause of end-stage renal disease. Early detection of DN can spare diabetic patients of severe complications. This study aimed to evaluate the diagnostic value of red cell distribution width (RDW) and neutrophil-lymphocyte ratio (NLR) in the detection of DN in patients with type 2 diabetes mellitus (T2DM). This cross-sectional study included a total of 130 patients with T2DM, already diagnosed with T2DM. The albumin creatinine ratio (ACR) in urine samples was calculated for each patient, according to which patients were divided into two groups: with evidence of DN when ACR ? 30 mg/g, and those with no evidence of DN when ACR < 30 mg/g. According to multivariate analysis, each of disease duration (OR
... Show MoreThe concrete industry consumes millions of tons of aggregate comprising of natural sands and gravels, each year. In recent years there has been an increasing trend towards using recycled aggregate to save natural resources and to produce lightweight concrete. This study investigates the possibility of using waste plastic as one of the components of lead-acid batteries to replace the fine aggregate by 50 and 70% by volume of concrete masonry units. Compared to the reference concrete mix, results demonstrated that a reduction of approximately 32.5% to 39.6% in the density for replacement of 50% to 70% respectively. At 28 days curing age, the compressive strength was decreased while the water absorption increased by increas
... Show MoreEstimations of average crash density as a function of traffic elements and characteristics can be used for making good decisions relating to planning, designing, operating, and maintaining roadway networks. This study describes the relationships between total, collision, turnover, and runover accident densities with factors such as hourly traffic flow and average spot speed on multilane rural highways in Iraq. The study is based on data collected from two sources: police stations and traffic surveys. Three highways are selected in Wassit governorate as a case study to cover the studied locations of the accidents. Three highways are selected in Wassit governorate as a case study to cover the studied locations of the accidents. The selection
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