##### Scholarly Book Review on Bayesian Statistics for Beginners: A Step-by-Step Approach

Eahsan Shahriary, Amir Hajibabaee

Asian Journal of Probability and Statistics, Page 1-4
DOI: 10.9734/ajpas/2020/v9i330226

This book offers the students and researchers a unique introduction to Bayesian statistics. Authors provide a wonderful journey in the realm of Bayesian Probability and aspire readers to become Bayesian statisticians. The book starts with Introduction to Probability and covers Bayes’ Theorem, Probability Mass Functions, Probability Density Functions, The Beta-Binomial Conjugate, Markov chain Monte Carlo (MCMC), and Metropolis-Hastings Algorithm. The book is very well written, and topics are very to the point with real-world applications but does not provide examples for computing using common open-source software.

##### Professional Development Needs to Improve Teaching Science in Secondary Schools: Case Study of Mbeya, Tanzania

Charles Ephraim Kibona, Joyce Sifa Ndabi, Isack Ephraim Kibona

Asian Journal of Probability and Statistics, Page 5-24
DOI: 10.9734/ajpas/2020/v9i330227

Aim: This study examined pedagogy and subject content needs for Professional Development (PD) to improve teachers’ skills in teaching science in secondary schools in Mbeya, Tanzania.

Study Design: The study employed a quantitative research approach and cross-sectional survey design.

Methodology: The main instrument used for the study was questionnaire. In this study, schools were randomly selected, and 256 respondents, science teachers were selected through stratified sampling technique. The data collected were analyzed quantitatively.

Results: Science teachers need Professional Development (PD) in Pedagogical Knowledge (PK), masterly of science subject contents and technological skills of modern teaching. There was no significant difference in the mean scores for components of pedagogy knowledge between teachers who teach math subject and those who teach physics, chemistry and biology at  using independent samples t-test. Teachers need of PD in subject content in topics were as follows: accounts (61.7%), genetics (46.2%), electromagnetism (44.2%), electronics (40.4%), circles and the Earth as a sphere (29.6%), statistics and probability (28.4%), inorganic chemistry (25%), and ionic theory and electrolysis (24.1%).

Conclusion: Science and mathematics teachers in Secondary schools need PD intervention in the subject content of science subjects.

##### Statistical Analysis of Tensile Strength and Flexural Strength Data from Universal Testing Machine

Asian Journal of Probability and Statistics, Page 54-62
DOI: 10.9734/ajpas/2020/v9i330230

The tensile strength and flexural strength are the most important mechanical properties as they provide the value of maximum tensile stress and flexural stress. The objective of this study is to analyze statistically the tensile strength and flexural strength data obtained from a universal testing machine. The tests were conducted upon a thermoplastic, specifically high-density polyethylene (HDPE), which was in-house molded by using an injection-molding machine. Three different persons have performed the tensile and flexural tests. Three other laboratories have also been involved in these tests. The relative standard deviation (RSD) values were calculated to express the precision and repeatability of the tests. Later, the standard score (z-score) values were also calculated to aid the comparison of the data. Finally, the single-factor analysis of variance (ANOVA) was employed to investigate statistically significant differences between the means of the tensile strength and flexural strength data of each person and laboratory. From the calculation, the RSD values of all three persons and laboratories were lower than 5%, indicating that the data were consistent. The z-score values of all three persons were within the range from -2 to 2, suggesting that the data were close to average. However, the z-score value for one of three laboratories was not within the range, demonstrating that the data was unusual. The P-values of all three persons were higher than 0.05 (except for flexural strength), implying that the difference between the means of the data was not statistically significant. Nevertheless, the P-values of all three laboratories were lower than 0.05, indicating that the difference between the means of the data was statistically significant.

##### A New Generalized Weibull- Odd Frѐchet Family of Distributions: Statistical Properties and Applications

A. Usman, S. I. S. Doguwa, B. B. Alhaji, A. T. Imam

Asian Journal of Probability and Statistics, Page 25-43
DOI: 10.9734/ajpas/2020/v9i330228

We introduced a new generalized Weibull- Odd Frѐchet family of distributions with three extra parameters and we derived some of its structural properties. We derived comprehensive mathematical properties which include moments, moment generating function, Entropies and Order Statistics. One family of this distribution called new generalized Weibull- Odd Frѐchet -Frѐchet distribution is used to fit two data sets using the MLE procedure. A Monte Carlo simulation is used to test the robustness of the parameters of this distribution, in terms of the bias and mean squared error. The results of fitting this new distribution to two different data sets suggest that the new distribution outperforms its competitors.

##### Solving Ordinary Differential Equation of Higher Order by Adomian Decomposition Method

Sumayah Ghaleb Othman, Yahya Qaid Hasan

Asian Journal of Probability and Statistics, Page 44-53
DOI: 10.9734/ajpas/2020/v9i330229

Aims/ Objectives: In this article, we use Adomian Decomposition method (ADM) for solving initial value problems in the higher order ordinary differential equations. Many researchers have used the ADM in order to find convergent as well as exact solutions of different types of equations. Therefore, the ADM is considered as an effective and successful method for solving differential equations. In this paper, we presented some suggested amendments to the ADM by using a new differential operator in order to find solutions for higher order types of equations. We demonstrated the effectiveness of this method through many examples and we find out that we get an approximate solutions using the proposed amendments. We can conclude that the suggested modification of ADM is afftective and produces reliable results.