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Sets And Probability Common Core Algebra 2 Homework



PBS Math Club helps you with your homework... and makes you laugh. They cover the 6th-9th grade Common Core Standard for math; topics like adding and subtracting integers, equations, ratios and proportions, and statistics. They use uncommon examples like Mean Girls to explain adding negative numbers in our show. These episodes way too long? Check out the "Instacram" clips for the :15 second versions. Math Club is produced for PBS Digital Studios and created by Radiant Features.




Sets And Probability Common Core Algebra 2 Homework



This lesson unit addresses common misconceptions relating to probability of simple and compound events. The lesson will help you assess how well students understand concepts of: Equally likely events; randomness; and sample sizes.


Samples and ProbabilityType of Unit: ConceptualPrior KnowledgeStudents should be able to:Understand the concept of a ratio.Write ratios as percents.Describe data using measures of center.Display and interpret data in dot plots, histograms, and box plots.Lesson FlowStudents begin to think about probability by considering the relative likelihood of familiar events on the continuum between impossible and certain. Students begin to formalize this understanding of probability. They are introduced to the concept of probability as a measure of likelihood, and how to calculate probability of equally likely events using a ratio. The terms (impossible, certain, etc.) are given numerical values. Next, students compare expected results to actual results by calculating the probability of an event and conducting an experiment. Students explore the probability of outcomes that are not equally likely. They collect data to estimate the experimental probabilities. They use ratio and proportion to predict results for a large number of trials. Students learn about compound events. They use tree diagrams, tables, and systematic lists as tools to find the sample space. They determine the theoretical probability of first independent, and then dependent events. In Lesson 10 students identify a question to investigate for a unit project and submit a proposal. They then complete a Self Check. In Lesson 11, students review the results of the Self Check, solve a related problem, and take a Quiz.Students are introduced to the concept of sampling as a method of determining characteristics of a population. They consider how a sample can be random or biased, and think about methods for randomly sampling a population to ensure that it is representative. In Lesson 13, students collect and analyze data for their unit project. Students begin to apply their knowledge of statistics learned in sixth grade. They determine the typical class score from a sample of the population, and reason about the representativeness of the sample. Then, students begin to develop intuition about appropriate sample size by conducting an experiment. They compare different sample sizes, and decide whether increasing the sample size improves the results. In Lesson 16 and Lesson 17, students compare two data sets using any tools they wish. Students will be reminded of Mean Average Deviation (MAD), which will be a useful tool in this situation. Students complete another Self Check, review the results of their Self Check, and solve additional problems. The unit ends with three days for students to work on Gallery problems, possibly using one of the days to complete their project or get help on their project if needed, two days for students to present their unit projects to the class, and one day for the End of Unit Assessment.


Prerequisites: Students must have a good upper level undergraduate math background including linear algebra, probability, and multi-variate calculus. Course work in numerical computation is desirable. Students should be able to do numerical programming in Python, C/C++, Java, Fortran, R, or Matlab. Students without experience in Python will have to put in some extra effort in the first few weeks.


This course provides a mathematical introduction to mechanics aimed at graduate students preparing for research on physical science topics in applied mathematics or applied probability. It covers fundamental core topics at an advanced mathematical level and it also provides examples of applications drawn from recent research.


Lecture, discussion, lab. The architecture and machine-level operations of modern computers at the logic, component, and system levels. Topics include integer, scaled, and floating point binary arithmetic; Boolean algebra and logic gates; control, arithmetic-logic, and pipeline units; addressing modes; cache, primary, and virtual memory; system buses; input-output and interrupts. Simple assembly language for a modern embedded processor is used to explore how common computational tasks are accomplished by a computer. Two lectures, one discussion, and one lab session per week. Laboratory exercises, homework exercises, in-class quizzes, two midterm exams, and a final exam. Prerequisite: CMPSCI 187 or ECE 242 or equivalent. Comment on Lab 1: Students registering for CMPSCI H01 must register for Lab 1.4 credits.


Machine learning is the computational study of methods for making statistically reliable inferences combining observed data and prior knowledge (models). This is a mathematically rigorous introduction to two major strands of research in machine learning: parametric approaches based on probabilistic graphical models, and nonparametric approaches based on kernel methods. Graphical models are a compact way of representing probability distributions over a large set ofdiscrete and continuous variables. "Learning" in parametric models corresponds to maximum likelihood estimation, i.e. find the parameters that maximize the likelihood of the data. By contrast, "learning" in nonparametric kernel-based models corresponds to finding a weighted sum of kernel functions applied to the data. Detailed course topics: mathematical foundations, Bayesian classifiers, maximum likelihood and maximum a posteriori (MAP) estimation, missing data and expectation maximization (EM), mixture models and hidden-Markov models, logistic regression and generalized linear models, maximum entropy and undirected graphical models, nonparametric models for densityestimation, reproducing kernel Hilbert spaces and the Representer theorem, margin classifiers and support vector machines, dimensionality reduction methods (PCA and LDA), computational learning theory, VC-dimension theory. State-of-the-art applications including bioinformatics, information retrieval, robotics, sensor networks and vision, will be used to illustrate the theory. There will be extensive homework exercises including mini-projects, a midterm, a final exam, and a group project. Prerequisites: undergraduate level probability and statistics, linear algebra, calculus, AI; computer programming in some high level language. 3 credits. 350c69d7ab


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