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.
Reading is one of the essential components of the English language. Countries that use English as a second language (ESL) sometimes have difficulties in reading and comprehension. According to many researches, mother tongue has proved some interferences with learning a second language. This study investigated the results of reading difficulties of young second language learners in terms of accuracy, comprehension, and rate using the Neale Analysis of Reading Ability test. The study was carried out in one of the High Schools for Boys in Hyderabad, India and included Grade five, aged 10-12 years. In order to understand the reading difficulties of English as a second language, a qualitative approach was employed. Interview, reading tes
... Show MoreDuring the 1970s, communicative view of language teaching began to be incorporated into syllabus design. The central question for the proponents of this view was: what does the learner want/need to do with the target language? This lead to the emergence of a teaching method (or approach) called communicative language teaching (CLT) during the late 1970s and early 1980s focusing on the functions that must be incorporated into a classroom. According to Brown (2001:43) CLT is a unified but broadly based, theoretically well informed set of tenets about the nature of language and of language learning and teaching. Harmer (2001:84) states that the communicative approach is the name which was given to a set of beliefs which included not only a
... Show MoreSecond language learner may commit many mistakes in the process of second language learning. Throughout the Error Analysis Theory, the present study discusses the problems faced by second language learners whose Kurdish is their native language. At the very stages of language learning, second language learners will recognize the errors committed, yet they would not identify the type, the stage and error type shift in the process of language learning. Depending on their educational background of English as basic module, English department students at the university stage would make phonological, morphological, syntactic, semantic and lexical as well as speech errors. The main cause behind such errors goes back to the cultural differences
... Show MoreThe aim of the current research is to recognizing the impact of mind and informational strategy on the achievement with the second intermediate students in the grammar of arabic language, the researcher used a partial-set experimental design and intentionally selected a sample out of the second intermediate class from (AL- Markazya Intermediate school) in the district of Hilla, affiliated which belongs to General Directorate of Babylon Education in the year (2020-2021) for applying the experiment. The sample was composed of (50) students, (25) ones for each group, the experimental group and normal one. The researcher balanced between the two groups in various changes including: (the chronological age counted by months, the academic achie
... Show MoreThis research aims to choose the appropriate probability distribution to the reliability analysis for an item through collected data for operating and stoppage time of the case study.
Appropriate choice for .probability distribution is when the data look to be on or close the form fitting line for probability plot and test the data for goodness of fit .
Minitab’s 17 software was used for this purpose after arranging collected data and setting it in the the program.
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... Show MoreFiber‐reinforced elastic laminated composites are extensively used in several domains owing to their high specific stiffness and strength and low specific density. Several studies were performed to ascertain the factors that affect the composite plates’ dynamic properties. This study aims to derive a mathematical model for the dynamic response of the processed composite material in the form of an annular circular shape made of polyester/E‐glass composite. The mathematical model was developed based on modified classical annular circular plate theory under dynamic loading, and all its formulas were solved using MATLAB 2023. The mathematical model was also verified with real experimental work involving the vibration test of the f
... Show MoreThis paper presents a computer simulation model of a thermally activated roof (TAR) to cool a room using cool water from a wet cooling tower. Modeling was achieved using a simplified 1-D resistance-capacitance thermal network (RC model) for an infinite slab. Heat transfer from the cooling pipe network was treated as 2-D heat flow. Only a limited number of nodes were required to obtain reliable results. The use of 6th order RC-thermal model produced a set of ordinary differential equations that were solved using MATLAB - R2012a. The computer program was written to cover all possible initial conditions, material properties, TAR system geometry and hourly solar radiation. The cool water supply was considered time
... Show MoreThe aim of study was making comparison in some kinematics variables in (100) meter butterfly swimming to first and second ranking in championship 2003 Espana, so noticed there is no such like this study in our country in comparison study for international champions therefore not specific and scientific discovering to these advanced levels, also the researchers depend on group of kinematics variables when the comparison making and it was included (50 meter the first, 50 meter the second, the differences between the first (50) meter and the second , more over basic variables in (100) meter butterfly , after having the results and treat it statistically the researchers reaches to two conclusions which was: • Success the first rank in startin
... Show MoreBACKGROUND: Genetic skeletal abnormalities are a heterogeneous group of genetic disorders frequently presenting with disproportionate short stature. AIM OF THE STUDY: To give an idea about the frequency of genetic skeletal abnormalities, and to find out whether these disorders are really increasing in the last 16 years or not. METHODS: During the period extending from (Jan, 1st 2003-April, 1st 2007), all cases of genetic skeletal disorders referred to the Genetic Counseling Clinic, Medical City – Baghdad who were born after 1991 were included in this study as the post-war group; the pre-war group, included all cases of skeletal disorders referred prior to 1991 (Jan., 1st 1987-Jan., 1st 1990). The demographic parameters, family history of
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