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.
In this work, excess properties (eg excess molar volume (VE), excess viscosity (ȠE), excess Gibbs free energy of activation of viscos flow (ΔG* E) and molar refraction changes (ΔnD) of binary solvent mixtures of tetrahydrofurfuryl alcohol (THFA) with aromatic hydrocarbons (benzene, toluene and p-xylene) have been calculated. This was achieved by determining the physical properties including density ρ, viscosity Ƞ and refraction index nD of liquid mixtures at 298.15 K. Results of the excess parameters and deviation functions for the binary solvent mixtures at 298.15 K have been discussed by molecular interactions that occur in these mixtures. Generally, parameters showed negative values and have been found to fit well to Redlich-Kister
... 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
In order to evaluate the performance of introduced varieties of maize and test them under different levels of plant density, and to determine which of the introduced varieties give a high yield and at what plant density, a field experiment was carried out at Station A in the Department of Field Crops- College of Agricultural Engineering Sciences - University of Baghdad- Jadiriyah, for the fall season 2021, the RCBD design was used with four replications, in a split plot arrangement, the three plant densities (50.000, 70.000, and 90.000 Plant s ha-1) were the main plates, while the varieties represented the secondary factor, which is six varieties of maize, class 2 = 5783 DKC, Class 3 = 6315 DKC, Class 4= 6590 DKC, whic
... Show MoreAn experimental investigation has been carried out for zinc-nickel (Zn-Ni) electro-deposition using the constant applied current technique. Weight difference approach method was used to determine the cathode current efficiency and deposit thickness. Also, the influence effect of current density on the deposition process, solderability, and porosity of the plating layer in microelectronic applications were examined. The bath temperature effect on nickel composition and the form of the contract was studied using Scanning Electron Microscope (SEM). Moreover, elemental nature of the deposition was analyzed by Energy Dispersive X-Ray (EDX).
It has been found that the best bath temperature
... Show MoreThe 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 MoreThe refractive indices, nD densities 𝜌, and viscosities of binary mixtures of sulfolane + n -butanol + sec- butanol + iso- butanol + tert – butanol + n-propanol and iso- propanol were measured at 298.15K. Form experimental data, excess molar volum VE , excess molar refractivity ∆nD, excess molar viscosity E and excess molar Gibbs free energy of activation of viscous flow G *E were calculated. From n-propanol – sulfolane and iso- propanol sulfolane mixtures showed negative ∆nD, n-butanol – sulfolane, sec-butanal – sulfolane, iso-butanol – sulfolane and tert- butanol sulfolane , nD was positive over the whole mole fraction rang , while VE , E and G *E show a negative deviation. The
... Show MoreAn 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 MoreThis 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
Samples 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
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 More