PPT-Binomial Theorem Keeper 10

Binomial Theorem Keeper 10 Honors Algebra II What Is a Factorial Evaluate the Factorial   Evaluate the Factorial   Evaluate   Evaluate the Factorial   Evaluate   Evaluate   Evaluate  . 1 binomialexpression isthesumordi64256erenceoftwotermsForexample 1 2 y a areallbinomialexpressions Ifwewanttoraiseabinomiale xpressiontoapowerhigherthan2 forexampleifwewantto64257nd 1 itisverycumbersometodothisbyrepeatedlymultiplying 1 byitselfInth Binomial Theorem Algebra 2/Trigonometry Reference SheetAlgebra 2/Trigonometry Sampler … Fall 09 Definition of Binomial coefficient. For nonnegative integers n and r with n . >. r the expansion (read “n above r”) is called a binomial coefficient and is defined by. Evaluating binomial coefficient . Probability Theorem. A binomial is a polynomial with two terms such as . x. + . a. . Often we need to raise a binomial to a power. In this section we'll explore a way to do just that without lengthy multiplication.. Counting. Fall . 2011. Sukumar Ghosh. The Product Rule. Example of Product Rule. Example of Product Rule. The Sum Rule. Example of Sum Rule. Example of Sum Rule. Wedding picture example. Counting subsets of a finite set. Reflection. What is a binomial?. A . binomial is a mathematical expression of two unlike terms with coefficients and which is raised to at least the power of. 1. . Examples of binomials are (. a+b. ), (x+2)^2, (a+c)^3, (y-4)^6. Karl L. Wuensch. Department of Psychology. East Carolina University. A Binomial . Experiment. consists of . n. identical trials.. each trial results in one of two outcomes, a “success” or a “failure.”. Distribution. If the probability that James is late home from work on any. day is 0.4, what is the probability that he is late home. t. hree times in a five-day working week?. L . L. . L. . L. ’ L’. Definition 1: . The . generation function . for the sequence. a. 0. , a. 1. , . . .,. a. k. . ,. . .. of real numbers is the infinite series . G(x) = a. 0. + a. 1. . x + . . .+ . a. k. x. k. +. . . =. Fall . 2011. Sukumar Ghosh. The Product Rule. Example of Product Rule. Example of Product Rule. The Sum Rule. Example of Sum Rule. Example of Sum Rule. Wedding picture example. Counting subsets of a finite set. What we learned last class…. We are not good at recognizing/dealing with randomness. Our “random” coin flip results weren’t streaky enough.. If B/G results behave like independent coin flips, we know how many families to EXPECT with 0,1,2,3,4 girls.. Algebra 2. Chapter 10. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. II. BINOMIAL DISTRIBUTIONS A. Binomial Experiments 1. A binomial experiment is a probability experiment that satisfies the following conditions: a. The experiment is repeated for a fixed number of independent trials. Chapter 8. Warm up. Find each combination or permutation. . 5 C 2. 10 C 3. 10 P 3. 8.1 The Binomial Distribution. A . binomial experiment. . is . statistical . experiment. that has the following properties: .