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.
Evaporation from water bodies is important and considered a major problem in dry and semi-dry regions, in this research the evaporation has been analyzed from two approaches: engineeringly and statistically. The engineering approach deals with the calculation of evaporation rates of Mosul Dam Lake. Three methods were used: pan evaporation class A, the combined and the mass-transfer. It was found that the values obtained by pan evaporation class A method was the highest among the other, while the mass transfer method achieved the lowest results. The evaporation rates during the year ranged according to the first method (0.9–5.5) mm/day, second (0.7–11.5) mm/day and the last method (1.0039×106) m3/year, whi
... Show MoreThe use of destructive weapons in wars without restrictions and controls, which eat green and dry land, pollute the environment and cause genocide, has become the problem of the times.
International conventions for the protection of the environment during armed conflicts are characterized by generality, ambiguity, and open to interpretation by the participating states in the agreement, and each state interprets these texts to serve its interests, but the Islamic Sharia stipulates the prohibition of the use of these comprehensive destructive weapons in an unambiguous manner, As stated in the Holy Quran:
... Show MoreA single step extraction-cleanup procedure using porous membrane-protected micro-solid phase extraction (μ-SPE) in conjunction with liquid chromatography–tandem mass spectrometry for the extraction and determination of aflatoxins (AFs) B1, B2, G1 and G2 from food was successfully developed. After the extraction, AFs were desorbed from the μ-SPE device by ultrasonication using acetonitrile. The optimum extraction conditions were: sorbent material, C8; sorbent mass, 20 mg; extraction time, 90 min; stirring speed, 1000 rpm; sample volume, 10 mL; desorption solvent, acetonitrile; solvent volume, 350 μL and ultrasonication period, 25 min without salt addition. Under the optimum conditions, enrichment factor of 11, 9, 9 and 10 for AFG2, AFG1
... Show MoreThe encoding of long low density parity check (LDPC) codes presents a challenge compared to its decoding. The Quasi Cyclic (QC) LDPC codes offer the advantage for reducing the complexity for both encoding and decoding due to its QC structure. Most QC-LDPC codes have rank deficient parity matrix and this introduces extra complexity over the codes with full rank parity matrix. In this paper an encoding scheme of QC-LDPC codes is presented that is suitable for codes with full rank parity matrix and rank deficient parity matrx. The extra effort required by the codes with rank deficient parity matrix over the codes of full rank parity matrix is investigated.
In the case where a shallow foundation does not satisfy with design requirements alone, the addition of a pile may be suitable to improve the performance of the foundation design. The lack of in-situ data and the complexity of the issues caused by lagging in the research area of pile foundations are notable. In this study, different types of piles were used under the same geometric conditions to determine the load-settlement relationships with various sandy soil relative densities. The ultimate pile capacity for each selected pile is obtained from a modified California Bearing Ratio (CBR) machine to be suitable for axial pile loading. Based on the results, the values of Qu for close-ended square pile were increased by 15
... Show MoreNuclear structure of 29-34Mg isotopes toward neutron dripline have been investigated using shell model with Skyrme-Hartree–Fock calculations. In particular nuclear densities for proton, neutron, mass and charge densities with their corresponding rms radii, neutron skin thicknesses and inelastic electron scattering form factors are calculated for positive low-lying states. The deduced results are discussed for the transverse form factor and compared with the available experimental data. It has been confirmed that the combining shell model with Hartree-Fock mean field method with Skyrme interaction can accommodate very well the nuclear excitation properties and can reach a highly descriptive and predictive power when investiga
... Show MoreThe nanocrystalline porous silicon (PS) films are prepared by electrochemical etching ECE of p -type silicon wafer with current density (10mA/cm ) and etching times on the formation nano -sized pore array with a dimension of around different etching time (10 and 20) min. The films were characterized by the measurement of XRD, atomic force microscopy properties (AFM). We have estimated crystallites size from X -Ray diffraction about nanoscale for PS and AFM confirms the nanometric size Chemical fictionalization during the electrochemical etching show on the surface chemical composition of PS. The atomic force microscopy investigation shows the rough silicon surface, with increasing etching process (current density and etching time) porous st
... Show MoreA dynamic experimental study of thermal decomposition of low density polyethylene has been carried out with two different heating rates .As usual , we can determine the activation energy of any polymer using( 3 - 6 ) TGA experiment as minimum , but in this work , we estimate the activation energy of LDPE using two of TGA experiments only
Abstract- Plasma parameters in a planar dc-sputtering discharge in argon were measured by cylindrical electrostatic probe (Langmuir probe).Electron density, electron temperature, floating potential, and space potential were monitored as a function of working discharge pressure. Electrostatic probe and supporting circuit were described and used to plot the current – voltage characteristics. Plasma properties were inferred from the current-voltage characteristics of a single probe positioned at the inter-cathode space. Typical values are in the range of (10-16 -10-17) m-3 and (2.93 – 5.3) eV for the electron density and the electron temperature respectively.
In this paper we present the first ever measured experimental electron momentum density of Cu2Sb at an intermediate resolution (0.6 a.u.) using 59.54 keV 241Am Compton spectrometer. The measurements are compared with the theoretical Compton profiles using density function theory (DFT) within a linear combination of an atomic orbitals (LCAO) method. In DFT calculation, Perdew-Burke-Ernzerhof (PBE) scheme is employed to treat correlation whereas exchange is included by following the Becke scheme. It is seen that various approximations within LCAO-DFT show relatively better agreement with the experimental Compton data. Ionic model calculations for a number of configurations (Cu+x/2)2(Sb-x) (0.0≤x≤2.0) are also performed utilizing free a
... Show More