An introduction to a beginners' guide to the world of probability and statistics in sciences. This is a beginner's guide with an emphasis on concepts, examples, and practical applications. It is designed for science students or undergraduates who have been exposed to basic probability and statistics from their courses but do not have any background in mathematics beyond basic calculus. The material covered can be used as a supplement for courses focusing on probability and statistics at the science or mathematics undergraduate level. Different applications of probability and statistics have been encountered in various branches of science and engineering. However, these applications have been carried out with a lack of understanding about the mathematical tools needed to perform the analysis. This book is designed to provide a basic review of probability and statistics as well as their historical development, so that the student will have a solid foundation upon which he or she can build his or her knowledge in these fields. The first part provides an introduction to concepts related to probability; the second part focuses on descriptive statistical analysis; and the third part discusses statistical analysis using inferential techniques. Chapter 1 introduces the basics of probability. This chapter has three sections. The first section presents elementary concepts of probability, including definitions, axioms, and interpretations of probability. The second section is devoted to the concept of statistical independence and frequency interpretation in terms of “long-run relative frequency” in which it illustrates in simple terms how to use basic information about probability in everyday situations that are encountered in life. The third section focuses on conditional probability. It presents three useful properties with an emphasis on their application to practical situations encountered in life, such as Bayes’ theorem, Pascal’s triangle, binomial distribution, hypergeometric distribution, multinomial distribution with an emphasis on practical applications. Chapter 2 is devoted to descriptive statistical analysis. The chapter has three sections, the first section is devoted to pre-analysis of data including the definitions and essential concepts of probability. It also presents various techniques for estimating distributions, including binomial, Poisson, and multinomial distributions. The second section presents a review of regression analysis and its applications in various fields such as budgeting, business planning, consumer behavior analysis, and forecasting. The third section discusses a variety of measures of central tendency used in data analysis such as arithmetic mean (comparing two populations), geometric mean (comparing two populations), median (comparing two groups), mode (describing the frequency or frequencies that will occur most frequently or least frequently in the set). Chapter 3 focuses on statistical analysis using inferential techniques. The chapter has two sections that include the use of inferential techniques for making decisions about the populations under investigation based on sample data. The first section focuses on basic concepts of hypothesis testing, including null hypothesis, alternative hypothesis, rejection region, Type I error rate (α), Type II error rate (β), power α/β or power curve, critical region, significance level (α), p-value and p-value table. The second section presents estimation by comparing sample data to parametric models including normal distribution, t distribution and F distribution.
1 Peter J.
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