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 paper we shall generalize fifth explicit Runge-Kutta Feldberg(ERKF(5)) and Continuous explicit Runge-Kutta (CERK) method using shooting method to solve second order boundary value problem which can be reduced to order one.These methods we shall call them as shooting Continuous Explicit Runge-Kutta method, the results are computed using matlab program.
A new, simple and sensitive method was used forevaluation of propranolol withphosphotungstic acidto prove the efficiency, reliability and repeatability of the long distance chasing photometer (NAG-ADF-300-2) using continuous flow injection analysis. The method is based on reaction between propranolol and phosphotungstic acid in an aqueous medium to obtain a yellow precipitate. Optimum parameters was studied to increase the sensitivity for developed method. A linear range for calibration graph was 0.007-13 mmol/L for cell A and 5-15 mmol/L for cell B, and LOD 207.4792 ng/160 µL and 1.2449 µg/160 µL respectively to cell A and cell B with correlation coefficient (r) 0.9988 for cell A, 0.9996 for cell B, RSD% was lower than 1%, (n=8) for the
... Show MoreA specific, sensitive and new simple method was used for the determination of methyldopa in pure and pharmaceutical formulations by using continuous flow injection analysis. This method is based on formation of ion pair compound between methyldopa and potassium hexacyanoferrate in acidic medium to obtain a yellow precipitate complex using long distance chasing photometer (NAG-ADF-300-2). The linear range for calibration graph was 0.05-35 mmol/L for cell A and 0.05-25 mmol/L for cell B, and LOD 1.4292 µg /200 µL for both cells with correlation coefficient (r) 0.9981 for cell A and 0.9994 for cell B, RSD% was lower than 0.5 % for n=8 for. The results were compared with classical method UV-Spectrophotometric at λ max=280 nm and turbi
... Show MoreThe main objective of the paper is to study the possibility of erecting 2 MW wind turbine in the south of Iraq (Barjisiah site) by utilizing WAsP model. Wind potential and output predicted the power of WT at a supposed site was calculated. The results for proposed WT showed the WT has a weak performance due to its high capacity and low potential of wind speeds at this site. So, the WT will provide power for a limited time during the year due to its operating at the zone under the rated wind speed.
PM3 and DFT (6-311G/ B3LYP) level calculations were carried out for the 5Radialene molecule, which is exhibit D5h symmetry. The obtained equilibrium geometry was applied for the calculation of all 3N−6 vibration frequencies, and for the analysis of its normal coordinates and symmetry species, in addition to some physical properties such as heat of formation, total energy, dipole moment and energy difference of HOMO and LUMO levels (ΔELUMO-HOMO), using Gaussian-03 program. The so calculated frequencies according to DFT (6-311G/ B3LYP) fall in the ranges;
CH2 str. (3016-3098 cm-1), C=C str. (1662-1709cm-1), ring (C-C str.) (1268-1464 cm-1). δCH2 (890-1317cm-1), (δCCC) (562-631cm-1), γCH2 (738-946cm-1) and γring (γCCC) (
In this study, different methods were used for estimating location parameter and scale parameter for extreme value distribution, such as maximum likelihood estimation (MLE) , method of moment estimation (ME),and approximation estimators based on percentiles which is called white method in estimation, as the extreme value distribution is one of exponential distributions. Least squares estimation (OLS) was used, weighted least squares estimation (WLS), ridge regression estimation (Rig), and adjusted ridge regression estimation (ARig) were used. Two parameters for expected value to the percentile as estimation for distribution f
... Show MoreTexture recognition is used in various pattern recognition applications and texture classification that possess a characteristic appearance. This research paper aims to provide an improved scheme to provide enhanced classification decisions and to decrease processing time significantly. This research studied the discriminating characteristics of textures by extracting them from various texture images using discrete Haar transform (DHT) and discrete Fourier transform DFT. Two sets of features are proposed; the first set was extracted using the traditional DFT, while the second used DHT. The features from the Fourier domain are calculated using the radial distribution of spectra, while for those extracted from Haar Wavelet the statistical
... Show MoreA cap of size and degree in a projective space, (briefly; (k,r)-cap) is a set of points with the property that each line in the space meet it in at most points. The aim of this research is to extend the size and degree of complete caps and incomplete caps, (k, r)-caps of degree r<12 in the finite projective space of dimension three over the finite field of order eleven, which already exist and founded by the action of subgroups of the general linear group over the finite field of order eleven and degree four, to (k+i,r+1) -complete caps. These caps have been classified by giving the t_i-distribution and -distribution. The Gap programming has been used to execute the designed algorit
... Show MoreThe study aimed to prepare rehabilitation exercises using some rubber ropes for people with partial rupture of the anterior cruciate ligament, to recognize their effect on the recovery of motor tides and to reduce the pain of those with partial rupture of the anterior cruciate ligament of the knee joint, and adopted the experimental method by designing the experimental and controlled groups on a sample of those with partial rupture of the anterior cruciate ligament of men (30-35) One year of those who attend the Physiotherapy Center/Rafidain University College of 12 injured were deliberately selected from their community of origin by (100%), and after determining the measuring tools and preparation of exercises applied with rubber r
... Show MoreEquilibrium Moisture sorption isotherms are very important in drying and storage analysis. Experimental moisture equilibrium data (adsorption and desorption) of Aspirin were determined using the static method of saturated salt solutions and that by exposing the material to different conditions of temperatures and water activities. Three different temperatures (25, 30, 40Cº) and water activities in the range of (6.3- 83.6%) were used. The results showed that the equilibrium moisture content increased with the increase in water activity at any temperature and decreased with temperature increase at constant water activity. The water activity increases with increasing in temperature when moisture content was kept constant. The sorption isot
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