This textbook is part of the OpenIntro Statistics series and offers complete coverage of the high school AP Statistics curriculum. Real data and plenty of inline examples and exercises make this an engaging and readable book. Links to lecture slides, video overviews, calculator tutorials, and video solutions to selected end of chapter exercises make this an ideal choice for any high school or Community College teacher. In fact, Portland Community College recently adopted this textbook for its Introductory Statistics course, and it estimates that this will save their students $250,000 per year. Find out more at: openintro.org/ahss

View our video tutorials here:
openintro.org/casio
openintro.org/TI

We hope readers will take away three ideas from this book in addition to forming a foundation
of statistical thinking and methods.

(1) Statistics is an applied field with a wide range of practical applications.
(2) You don't have to be a math guru to learn from real, interesting data.
(3) Data are messy, and statistical tools are imperfect. But, when you understand the strengths and weaknesses of these tools, you can use them to learn about the real world.
Textbook overview
The chapters of this book are as follows:

1. Data collection. Data structures, variables, and basic data collection techniques.
2. Summarizing data. Data summaries and graphics.
3. Probability. The basic principles of probability.
4. Distributions of random variables. Introduction to key distributions, and how the normal model applies to the sample mean and sample proportion.
5. Foundation for inference. General ideas for statistical inference in the context of estimating the population proportion.
6. Inference for categorical data. Inference for proportions using the normal and chisquare distributions.
7. Inference for numerical data. Inference for one or two sample means using the t distribution, and comparisons of many means using ANOVA.
8. Introduction to linear regression. An introduction to regression with two variables.
Instructions are also provided in several sections for using Casio and TI calculators.

This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired.

In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks.

Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals).

Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.

Table of Contents
1 Preface
2 Probability Systems
3 Minterm Analysis
4 Conditional Probability
5 Independence of Events
6 Conditional Independence
7 Random Variables and Probabilities
8 Distribution and Density Functions
9 Random Vectors and joint Distributions
10 Independent Classes of Random Variables
11 Functions of Random Variables
12 Mathematical Expectation
13 Variance, Covariance, Linear Regression
14 Transform Methods
15 Conditional Expectation, Regression
16 Random Selection
17 Conditional Independence, Given a Random Vector
18 Appendices

Biology 2e is designed to cover the scope and sequence requirements of a typical two-semester biology course for science majors. The text provides comprehensive coverage of foundational research and core biology concepts through an evolutionary lens. Biology includes rich features that engage students in scientific inquiry, highlight careers in the biological sciences, and offer everyday applications. The book also includes various types of practice and homework questions that help students understand—and apply—key concepts. The 2nd edition has been revised to incorporate clearer, more current, and more dynamic explanations, while maintaining the same organization as the first edition. Art and illustrations have been substantially improved, and the textbook features additional assessments and related resources.

By the end of this section, you will be able to do the following:

Describe the scientific reasons for the success of Mendel’s experimental work
Describe the expected outcomes of monohybrid crosses involving dominant and recessive alleles
Apply the sum and product rules to calculate probabilities

Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance.

This course emphasizes three methodologies - reliability and probabilistic risk assessment (RPRA), decision analysis (DA), and cost-benefit analysis (CBA). In this class, the issues of interest are: the risks associated with large engineering projects such as nuclear power reactors, the International Space Station, and critical infrastructures; the development of new products; the design of processes and operations with environmental externalities; and infrastructure renewal projects.

Chapter 1 – Linear Functions in Business and Economics
Chapter 2 – Solving Systems of Linear Equations
Chapter 3 – Matrices
Chapter 4 – Linear Programming
Chapter 5 – The Mathematics of Finance
Chapter 6 – Introduction to Statistics
Chapter 7 – Introduction to Probability
Chapter 8 – Counting Principles
Chapter 9 – Introduction to Probability Distributions

Includes a Finite Mathematics Workbook: https://math-faq.com/wp/finite-mathematics-workbook/ . In each workbook, you will find key terms, a short summary, and guided problems for each section in the ebook. Accompanying each guided example is a practice problem for students to complete. Answers to the practice problems are available at the end of each chapter’s workbook.

Continues 18.100. Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals.

" An historical examination and analysis of the evolution and development of games and game mechanics. Topics include a large breadth of genres and types of games, including sports, game shows, games of chance, schoolyard games, board games, roleplaying games, and digital games. Students submit essays documenting research and analysis of a variety of traditional and eclectic games. Project teams required to design, develop, and thoroughly test their original games."

Unified theory of information with applications to computing, communications, thermodynamics, and other sciences. Digital signals and streams, codes, compression, noise, and probability. Reversible and irreversible operations. Information in biological systems. Channel capacity. Maximum-entropy formalism. Thermodynamic equilibrium, temperature. The Second Law of Thermodynamics. Quantum computation.

Ancillary materials for interactive statistics:

1: Random Number Generator
2: Completing a Frequency, Relative, and Cumulative Relative Frequency Table Activity
3: The Box Plot Creation Game
4: Online Calculator of the Mean and Median
5: Online Mean, Median, and Mode Calculator From a Frequency Table
6: Standard Deviation Calculator
7: Guess the Standard Deviation Game
8: Mean and Standard Deviation for Grouped Frequency Tables Calculator
9: Z-Score Calculator
10. Expected Value and Standard Deviation Calculator
11: Be the Player Or the Casino Expected Value Game
12: Binomial Distribution Calculator
13: Normal Probability Calculator
14: Calculator For the Sampling Distribution for Means
15: Discover the Central Limit Theorem Activity
16: Sampling Distribution Calculator for Sums
17: Observe the Relationship Between the Binomial and Normal Distributions
18: Confidence Interval Calculator for a Mean Calculator With Statistics (Sigma Unknown)
19: Visually Compare the Student's t Distribution to the Normal Distribution
20: Sample Size for a Mean Calculator
21: Confidence Interval for a Mean (With Data) Calculator
22: Interactively Observe the Effect of Changing the Confidence Level and the Sample Size
23: Confidence Interval for a Mean (With Statistics) Calculator
24: Confidence Interval Calculator for a Population Mean (With Data, Sigma Unknown)
25: Confidence Interval For Proportions Calculator
26: Needed Sample Size for a Confidence Interval for a Population Proportion Calculator
27: Hypothesis Test for a Population Mean Given Statistics Calculator
28: Hypothesis Test for a Population Mean With Data Calculator
29: Hypothesis Test for a Population Proportion Calculator
30: Two Independent Samples With Data Hypothesis Test and Confidence Interval Calculator
31: Two Independent Samples With Statistics and Known Population Standard Deviations Hypothesis Test and Confidence Interval Calculator
32: Two Independent Samples With Statistics Calculator
33: Hypothesis Test and Confidence Interval Calculator: Difference Between Population Proportions
34: Hypothesis Test and Confidence Interval Calculator for Two Dependent Samples
35: Visualize the Chi-Square Distribution
36: Chi-Square Goodness of Fit Test Calculator
37: Chi-Square Test For Independence Calculator
38: Chi-Square Test For Homogeneity Calculator
39: Scatter Plot Calculator
40: Scatter Plot, Regression Line, r,and r^2 Calculator
41: Full Regression Analysis Calculator
42: Shoot Down Money at the Correct Correlation Game
43: Visualize How Changing the Numerator and Denominator Degrees of Freedom Changes the Graph of the F-Distribution
44: ANOVA Calculator
45: Central Limit Theorem Activity

In this course, the student will learn the basic terminology and concepts of probability theory, including sample size, random experiments, outcome spaces, discrete distribution, probability density function, expected values, and conditional probability. The course also delves into the fundamental properties of several special distributions, including binomial, geometric, normal, exponential, and Poisson distributions. Upon successful completion of this course, the student will be able to: Define probability, outcome space, events, and probability functions; Use combinations to evaluate the probability of outcomes in coin-flipping experiments; Calculate the union of events and conditional probability; Apply Bayes's theorem to simple situations; Calculate the expected values of discrete and continuous distributions; Calculate the sums of random variables; Calculate cumulative distributions and marginal distributions; Evaluate random processes governed by binomial, multinomial, geometric, exponential, normal, and Poisson distributions; Define the law of large numbers and the central limit theorem. (Mathematics 252)

Introduction to Statistics is a resource for learning and teaching introductory statistics. This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible. Please cite as: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Instructor's manual, PowerPoint Slides, and additional questions are available.

This course covers descriptive statistics, the foundation of statistics, probability and random distributions, and the relationships between various characteristics of data. Upon successful completion of the course, the student will be able to: Define the meaning of descriptive statistics and statistical inference; Distinguish between a population and a sample; Explain the purpose of measures of location, variability, and skewness; Calculate probabilities; Explain the difference between how probabilities are computed for discrete and continuous random variables; Recognize and understand discrete probability distribution functions, in general; Identify confidence intervals for means and proportions; Explain how the central limit theorem applies in inference; Calculate and interpret confidence intervals for one population average and one population proportion; Differentiate between Type I and Type II errors; Conduct and interpret hypothesis tests; Compute regression equations for data; Use regression equations to make predictions; Conduct and interpret ANOVA (Analysis of Variance). (Mathematics 121; See also: Biology 104, Computer Science 106, Economics 104, Psychology 201)

The main goal of the course is to highlight the general assumptions and methods that underlie all statistical analysis. The purpose is to get a good understanding of the scope, and the limitations of these methods. We also want to learn as much as possible about the assumptions behind the most common methods, in order to evaluate if they apply with reasonable accuracy to a given situation. Our goal is not so much learning bread and butter techniques: these are pre-programmed in widely available and used software, so much so that a mechanical acquisition of these techniques could be quickly done "on the job". What is more challenging is the evaluation of what the results of a statistical procedure really mean, how reliable they are in given circumstances, and what their limitations are.Login: guest_oclPassword: ocl

Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.

The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."