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.
Lithium doped Nickel-Zinc ferrite material with chemical formula Ni0.9−2x Zn0.1LixFe2+xO4, where x is the ratio of lithium ions Li+ (x = 0, 0.01, 0.02, 0.03 and 0.04) prepared by using sol-gel auto combustion technique. X-ray diffraction results showed that the material have pure cubic spinal structure with space group Fd-3m. The experimental values of the lattice constant (aexp) were decreased from 8.39 to 8.35 nm with doped Li ions. It was found that the decreasing of the crystallite size with addition of lithium ions concentration. The radius of tetrahedral (rtet) and octahedral (roct) site were computed from cation distribution. SEM images have been taken to show the morphology of compound. The dielectric parameters [dissipation fa
... Show MoreIn this study we examine variations in the structure of perovskite compounds of LaBa2Cu2O9, LaBa2CaCu3O12 and LaBa2Ca2Cu5O15 synthesized using the solid state reaction method. The samples’ compositions were assessed using X-ray fluorescence (XRF) analysis. The La: Ba: Ca: Cu ratios for samples LaBa2Cu2O9, LaBa2CaCu3O12 and LaBa2Ca2Cu5O15 were found by XRF analysis to be around 1:2:0:2, 1:2:1:3, and 1:2:2:5, respectively. The samples’ well-known structures were then analyzed using X-ray diffraction. The three samples largely consist of phases 1202, 1213, and 1225, with a trace quantity of an unknown secondary phase, based on the intensities and locations of the diffraction peaks. According to the measured parameters a, b, and c, every sa
... Show MoreThe long – term behaviour of polyethylene products used out doors is affected by weathering. In the present work,
weathering test was carried out to find the effect of the environment conditions on the mechanical properties of
HDPE/LLDPE blends with different weight percents (0, 15, 30, and 45 %) relative to the LLDPE by increasing the
exposure times to (100, 150, 200, 250, 300) hr.
A series of tests (destructive), tensile, impact and hardness were carried out on the prepared samples, the results
obtained declare the changes on the material behaviour from ductile to brittle and the polymer shows a decline in the
mechanical properties with increasing the exposure times.
In the present work empirical equations were r
This study was conducted to determining the variable effects on water quality of Greater Zab River in Erbil province, Iraq, using multivariate statistical analysis. Seventeen variables were monitored in four sampling sites during one year (from May 2012 to April 2013). The dataset were treated using principal component analysis (PCA)/ factor analysis (FA), cluster analysis (CA) to the most important factors affecting water quality, sources of pollution and suitability of water for drinking consumption and irrigation. Six factors were identified as responsible for the data structure explaining 73.5% of the total variance in the dataset and are conditionally named, hydrochemical from weathering, mineral salts and domestic wastes. CA showed
... Show MoreAbstract
Corrosion-fatigue occurs by the combined actions of cyclic loading and corrosive environment. The effect of shot peening on cumulative corrosion-fatigue life of 1100-H12 Al alloy was investigated. Before fatigue testing, specimens were submerged in 3.5%NaCl solution for 71 days. Constant fatigue tests were performed with and without corrosive environment. Cumulative corrosion-fatigue tests were also carried out in order to determine the fatigue life before and after shot peening. The constant fatigue life was significantly reduced due to corrosive environment and the endurance fatigue limit was reduced by 13% compared with dry fatigue. In case of shot peening the cumul
... Show MoreThe energy expectation values for Li and Li-like ions ( , and ) have been calculated and examined within the ground state and the excited state in position space. The partitioning technique of Hartree-Fock (H-F) has been used for existing wave functions.
The present study aimed to investigate the effect of re-operations engineering business in continuous improvement, as the rapid development of service activities generally private and the great diversity in the goals of its operations and programs of the university and the service has led to the increasing importance of re-operations engineering business as well as continuous improvement so began to study the relationship between the re engineering and continuous improvement of university service, and applied study on a sample of professors from the faculties of administration, economics and law. Find and reach to several conclusions, notably that the preparation of the teaching staff training sessions on how to use modern teaching
... Show MoreThe radial wavefunctions of transformed harmonic-oscillator in the local scale transformation technique are used to calculate the root-mean square proton, charge, neutron and matter radii, nuclear density distributions and elastic electron scattering charge form factors of stable (10,11B) and (unstable) exotic (8,14,17B) Boron isotopes. For 10B and 11B, the transformed harmonic-oscillator wavefunctions are applied to all subshells in no-core shell model approach using wbp interaction. For 8,14,17B, the radial wavefunctions of harmonic-oscillator and THO are used to calculate the aforementioned quantities for the core and halo parts, respectively. The calculate
... Show MoreThis paper studies the combination of fluid viscous dampers in the outrigger system to add supplementary damping into the structure, which purpose to remove the dependability of the structure to lower variable intrinsic damping. This optimizes the accuracy of the dynamic response and by providing higher level of damping, basically minimizes the wanted stiffness of the structure while at the same time optimizing the achievement.
The modal considered is a 36 storey square high rise reinforced concrete building. By constructing a discrete lumped mass model and using frequency-based response function, two systems of dampers, parallel and series systems are studied. The maximu
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