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.
An effective two-body density operator for point nucleon system folded with two-body correlation functions, which take account of the effect of the strong short range repulsion and the strong tensor force in the nucleon-nucleon forces, is produced and used to derive an explicit form for ground state two-body charge density distributions (2BCDD's) and elastic electron scattering form factors F (q) for 19F, 27Al and 25Mg nuclei. It is found that the inclusion of the two-body short range correlations (SRC) has the feature of reducing the central part of the 2BCDD's significantly and increasing the tail part of them slightly, i.e. it tends to increase the probability of transferring the protons from the central region of the nucleus towards
... Show MoreTo 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 MoreAbstractIn the field of construction materials the glass reinforced mortar and Styrene Butadiene mortar are modern composite materials. This study experimentally investigated the effect of addition of randomly dispersed glass fibers and layered glass fibers on density and compressive strength of mortar with and without the presence of Styrene Butadiene Rubber (SBR). Mixtures of 1:2 cement/sand ratio and 0.5 water/cement ratio were prepared for making mortar. The glass fibers were added by two manners, layers and random with weight percentages of (0.54, 0.76, 1.1 and 1.42). The specimens were divided into two series: glass-fiber reinforced mortar without SBR and glass-fiber reinforced mortar with 7% SBR of mixture water. All s
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The poor hole cleaning efficiency could causes many problems such as high torque, drag, poor hydraulics and pipe stuck. These inherent problems result in an avoidable high operation cost which this study tried to address. In this study, the effect of cutting density on hole cleaning efficiency in deviated and horizontal wells was investigated. Experiments were conducted using 40 feet (12 m) long of flow loop made from iron and PVC. However, the test section was made from PVC with (5.1m) long and (4” ID) for outer pipe and (2” OD) inner pipe. The cutting transport ratio (CTR) was determined from weight measurements for each test. Cutting Transport Ratio has been investigated for effects of the following parameters; flow rate, cu
... Show MoreReactive Powder Concrete (RPC) could be considered as the furthermost significant modern high compressive strength concrete. In this study, an experimental investigation on the impact of micro steel fiber volume fraction ratio and gamma ray irradiation duration influence upon the compressive strength of RPC is presented. Three volume fraction ratios (0.0, 1.0 and 1.5) % was implemented. For each percentage of the adopted fiber ratios, six different irradiation duration was considered; these are (1, 2, 3, 4, 5 and 6) days. Gamma source (Cs-137) of energy (0.662) MeV and activity (6) mci was used. In a case of zero volume fraction ratio, the experimental results showed that gamma ray had a significant influence on the reducing of the
... Show MoreUtilizing the Turbo C programming language, the atmospheric earth model is created from sea level to 86 km. This model has been used to determine atmospheric Earth parameters in this study. Analytical derivations of these parameters are made using the balancing forces theory and the hydrostatic equation. The effects of altitude on density, pressure, temperature, gravitational acceleration, sound speed, scale height, and molecular weight are examined. The mass of the atmosphere is equal to about 50% between sea level and 5.5 km. g is equal to 9.65 m/s2 at 50 km altitude, which is 9% lower than 9.8 m/s2 at sea level. However, at 86 km altitude, g is close to 9.51 m/s2, which is close to 15% smaller than 9.8 m/s2. These resu
... Show MoreSamples of Bi1.6Pb0.4Sr2Ca2Cu3O10+δ superconductor were prepared by solid-state reaction method to study the effects of gold nanoparticles addition to the superconducting system, Nano-Au was introduced by small weight percentages (0.25, 0.50, 0.75, 1.0, and 1.25 weight %). Phase identification and microstructural
characterization of the samples were investigated using XRD and SEM. Moreover, DC electrical resistivity as a function of the temperature, critical current density Jc, AC magnetic susceptibility, and DC magnetization measurements were carried to evaluate the relative performance of samples. x-ray diffraction analysis showed that both (Bi,Pb)-2223 and Bi-2212 phases coexist in the samples having an orthorhombic crystal struct
The present project involves photodegrading the dye solochrom violet under advanced oxidation techniques at (25 oC) temperature and UV light. Zinc Oxide (ZnO) and UV radiation at a wavelength of 580 nm were used to conduct the photocatalytic reaction of the solochrom violet dye. One of the factors looked into was the impact of the starting conditions. pH, the amount of original hydrogen peroxide, and the dye concentration time radiation were used. For hours, the kinetics and percentages of degradation were examined at various intervals. In general, it has been discovered that the photodegradation rates of the dye were greater when H2O2 and ZnO were combined with UV light. The best wavelength to use was determined. Modern oxidation techni
... Show MoreIn an earlier paper, the basic analytical formula for particle-hole nuclear state densities was derived for non-Equidistant Spacing Model (non-ESM) approach. In this paper, an extension of the former equation was made to include pairing. Also a suggestion was made to derive the exact formula for the particle-hole state densities that depends exactly on Fermi energy and nuclear binding energies. The results indicated that the effects of pairing reduce the state density values, with similar dependence in the ESM system but with less strength. The results of the suggested exact formula indicated some modification from earlier non-ESM approximate treatment, on the cost of more calculation time
This study was undertaken to provide more insight on the optimum injection temperature used for the production of PE crates, thereby saving time and money, and improving part quality. The work included processing trails of HDPE crates in an injection
molding machine at five temperatures ranged from 220 to 300°C. Both Rheological and mechanical characterization was conducted in order to understand the effect of injection temperature on the properties of crates. Oven aging was also applied for (4 weeks) to evaluate the long-term thermal stability. The results revealed that producing the crates at a temperature range of (260-280 °C) gives the best rheological and mechanical result. The lowest drop in thermal stability has been observed