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.

Econometrics is the study of estimation and inference for economic models using economic data. Econometric theory concerns the study and development of tools and methods for applied econometric applications. Applied econometrics concerns the application of these tools to economic data.

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.

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."

This course will provide students with an in-depth understanding of the fundamental concepts and computational methods of statistics. These concepts will be developed through the question of how to estimate an unknown quantity using sample data. Students will learn to incorporate the foundational concepts of mathematics with statistical analysis to describe and solve real-life problems and questions. The topics addressed include: displaying categorical data using tables, bar graphs, and circle graphs; drawing conclusions about categorical data; displaying quantitative data using dot plots, stem-and-leaf plots, histograms and box-and-whisker plots; describing data distributions using measures of center (mode, mean, and median) and measures of spread (standard deviation, range and IQR); Displaying bivariate data using scatterplots; analyzing bivariate data using linear regression; elementary probability; normal probability distributions, sampling distributions; confidence intervals and hypothesis testing of the proportion and the mean.

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.

This text can be used for Math 241 (Introduction to Probability and Mathematical Statistics) at Queens College. Topics include the axioms of probability, counting, conditional probabilities, random variables, and an introduction to statistics.

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)

This course will provide students with an in-depth understanding of the fundamental concepts and computational methods of statistics. These concepts will be developed through the question of how to estimate an unknown quantity using sample data. Students will learn to incorporate the foundational concepts of mathematics with statistical analysis to describe and solve real-life problems and questions. The topics addressed include: displaying categorical data using tables, bar graphs, and circle graphs; drawing conclusions about categorical data; displaying quantitative data using dot plots, stem-and-leaf plots, histograms and box-and-whisker plots; describing data distributions using measures of center (mode, mean, and median) and measures of spread (standard deviation, range and IQR); Displaying bivariate data using scatterplots; analyzing bivariate data using linear regression; elementary probability; normal probability distributions, sampling distributions; confidence intervals and hypothesis testing of the proportion and the mean.

In this class, students use data and systems knowledge to build models of complex socio-technical systems for improved system design and decision-making. Students will enhance their model-building skills, through review and extension of functions of random variables, Poisson processes, and Markov processes; move from applied probability to statistics via Chi-squared t and f tests, derived as functions of random variables; and review classical statistics, hypothesis tests, regression, correlation and causation, simple data mining techniques, and Bayesian vs. classical statistics. A class project is required.

Decision-Making often refers to a multi-stage process that starts with some form of introspection or reflection about a situation in which a person or group of people find themselves. These ruminations usually lead to series of questions that need to be answered, or to a set of data that needs to be collected and analyzed, or to some calculations that need to be performed before someone can be in a position to make informed decisions and take appropriate actions.We provide some simple examples of Quantitative Models, which are often found in a decision-making situation. We focus on the use of algebraic equations, probability models, the “Payoff Table” and “Decision Tree” models, to represent situations involving a sequence one or more of decisions over time. Concepts are illustrated with a large set of examples that can be presented during classroom instruction and can be practiced by the students, either individually or in groups, through homework or lab exercises.

Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example: The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of "The Ten Things Everyone Should Know About Science". A recent Scientific American article argues that statistical literacy is crucial in making health-related decisions. Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and Netflix to the Office of Management and Budget. The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.

Interpretations of the concept of probability. Basic probability rules; random variables and distribution functions; functions of random variables. Applications to quality control and the reliability assessment of mechanical/electrical components, as well as simple structures and redundant systems. Elements of statistics. Bayesian methods in engineering. Methods for reliability and risk assessment of complex systems, (event-tree and fault-tree analysis, common-cause failures, human reliability models). Uncertainty propagation in complex systems (Monte Carlo methods, Latin Hypercube Sampling). Introduction to Markov models. Examples and applications from nuclear and chemical-process plants, waste repositories, and mechanical systems. Open to qualified undergraduates.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

" This course develops logical, empirically based arguments using statistical techniques and analytic methods. Elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation are covered. Emphasis is on the use and limitations of analytical techniques in planning practice."