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, an algorithm for binary codebook design has been used in vector quantization technique, which is used to improve the acceptability of the absolute moment block truncation coding (AMBTC) method. Vector quantization (VQ) method is used to compress the bitmap (the output proposed from the first method (AMBTC)). In this paper, the binary codebook can be engender for many images depending on randomly chosen to the code vectors from a set of binary images vectors, and this codebook is then used to compress all bitmaps of these images. The chosen of the bitmap of image in order to compress it by using this codebook based on the criterion of the average bitmap replacement error (ABPRE). This paper is suitable to reduce bit rates
... Show MoreNow that most of the conventional reservoirs are being depleted at a rapid pace, the focus is on unconventional reservoirs like tight gas reservoirs. Due to the heterogeneous nature and low permeability of unconventional reservoirs, they require a huge number of wells to hit all the isolated hydrocarbon zones. Infill drilling is one of the most common and effective methods of increasing the recovery, by reducing the well spacing and increasing the sweep efficiency. However, the problem with drilling such a large number of wells is the determination of the optimum location for each well that ensures minimum interference between wells, and accelerates the recovery from the field. Detail
A mathematical model has been formulated to predict the influence of high outdoor air temperature on the performance of small scale air - conditioning system using R22 and alternative refrigerants R290, R407C, R410A. All refrigerants were investigated in the cooling mode operation. The mathematical model results have been validated with experimental data extracted from split type air conditioner of 2 TR capacity. This entailed the construction of an experimental test rig which consists of four main parts. They are, the refrigeration system, psychrometric test facility, measuring instrumentation, and auxiliary systems. The conditioned air was maintained at 25 0C dry bulb and 19 0C wet bulb for all tests. The outdoor ambient air temperatur
... Show MoreIn this study, Zizphus spina-christi leaf powder was applied for the adsorption of methyl orange. The effect of different operating parameters on the Batch Process adsorption was investigated such as solution pH (2-12), effect of contact time (0-60 min.), initial dye concentration (2-20 mg/L), effect of adsorbent dosage (0-4.5 g) and effect of temperature (20-50ᵒC). The results show a maximum removal rate and adsorption capacity (%R= 23.146, qe = 2.778 mg/g) at pH = 2 and equilibrium was reached at 40 min. The pseudo- second-order kinetics were found to be best fit for the removal process (R2 = 0.997). Different isotherm models (Langmuir, Freundlich, Dubini-Radushkevich,Temkin) were applied in this stud
... Show MoreImage quality has been estimated and predicted using the signal to noise ratio (SNR). The purpose of this study is to investigate the relationships between body mass index (BMI) and SNR measurements in PET imaging using patient studies with liver cancer. Three groups of 59 patients (24 males and 35 females) were divided according to BMI. After intravenous injection of 0.1 mCi of 18F-FDG per kilogram of body weight, PET emission scans were acquired for (1, 1.5, and 3) min/bed position according to the weight of patient. Because liver is an organ of homogenous metabolism, five region of interest (ROI) were made at the same location, five successive slices of the PET/CT scans to determine the mean uptake (signal) values and its standard deviat
... Show MoreMango fruit is one of the most nutritionally rich fruits with unique flavor, this fruit belonged to family of Anacardiaceae and it is an excellent source of vitamins specially vitamin A, carotene pigments and potassium. In this study the antimicrobial activity of mango seeds extract has been investigated against gram positive bacteria (Staphylococcus aureus and Bacillus spp.) and gram negative bacteria (Pseudomonas aeruginosa and E. coli) and yeast Candida albicans by well diffusion method in nutrient agar and the results were expressed as the diameter of bacterial inhibition zones surrounding the wells, and the antibiofilm of its extracts was observed against Staphylococcus aureus. The seeds extractions prepared by two solvents: 8
... Show MoreA mathematical model was proposed to study the microkinetics of esterification reaction of oleic acid with ethanol over prepared HY zeolite catalyst. The catalyst was prepared from Iraqi kaolin source and its properties were characterized by different techniques. The esterification was done under different temperature (40 to 70˚C) with 6:1 for molar ratio of ethanol to oleic acid and 5 % catalyst loading.
The microkinetics study was done over two period of time each period was examined individually to calculate the reaction rate constant and activation energy. The impact of the mass transfer resistance to the reactant was also investigated; two different studies have been accomplished to do this purpose.
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The study of oxygen mass transfer was conducted in a laboratory scale 5 liter stirred bioreactor equipped with one Rushton turbine impeller. The effects of superficial gas velocity, impeller speed, power input and liquid viscosity on the oxygen mass transfer were considered. Air/ water and air/CMC systems were used as a liquid media for this study. The concentration of CMC was ranging from 0.5 to 3 w/v. The experimental results show that volumetric oxygen mass transfer coefficient increases with the increase in the superficial gas velocity and impeller speed and decreases with increasing liquid viscosity. The experimental results of kla were correlated with a mathematical correlation des
... Show MoreIn the present work experiments were conducted to study the effect of solid loading (1,5 and 9 vol.%) on the enhancement of carbon dioxide absorption in bubble column at various volumetric gas flow rate (0.75, 1 and 1.5 m3/h) and absorbent concentration (caustic soda)( 0.1,0.5 and 1 M ). Activated carbon and alumina oxide (Al2O3) are used as solid particles. The Danckwerts method was used to calculate interfacial area and individual mass transfer coefficients during absorption of carbon dioxide in a bubble column. The results show that the absorption rate was increased with increasing volumetric gas flow rate, caustic soda concentration and solid loading. Mass transfer coefficient and interfac
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