Chapter 8 Additional Probability Topics
|
|
- Kerry Caldwell
- 6 years ago
- Views:
Transcription
1 Chapter 8 Additional Probability Topics 8.6 The Binomial Probability Model Sometimes experiments are simulated using a random number function instead of actually performing the experiment. In Problems 76 79, use a graphing utility to simulate each experiment. 77. Tossing a Loaded Coin Consider the experiment of tossing a loaded coin 4 times and counting the number of heads occurring in these 4 tosses. Simulate the experiment using a random number function on your calculator, considering a toss to be tails (T) if the result is less than 0.80 and considering a toss to be heads (H) if the result is greater than or equal to Record the number of heads in 4 tosses. [Note: Most calculators repeat the action of the last entry if you simply press the ENTER, or EXE, key again.] Repeat the experiment times, obtaining a sequence of numbers. Using these numbers, you can estimate the P k, for each k = 0,1, 2, 3, 4 by the ratio probability of k heads, ( ) Number of times k appears in your sequence Enter your estimates in a table. Calculate the actual probabilities using the binomial probability formula and enter these numbers in the table. How close are your numbers to the actual values? k Your Estimate of P(k) Actual Value of P(k)
2 Recall from Chapter 7, we can generate random numbers using the rand command. To simulate tossing the coin four times, use rand(4), store the results in the list L1, and go to the data editor under to view the results. Remember that we are using a random number generator, so your results will most likely differ from the results shown below. One entry in the list is greater than 0.8, so our result for our first trial is 1. Return to the home screen and press Í to repeat the experiment again. This time there were no entries in the list greater than 0.8, so the result from our second trial is 0. Again, there were no entries in the list greater than 0.8, so the result from our third trial is 0. 76
3 Again, there were no entries greater than 0.8, so the result from our fourth trial is 0. This time there was only one entry greater than 0.8, so the result from our fifth trial is 1. This time there were no entries greater than 0.8, so the result from our sixth trial is 0. Again, there were no entries greater than 0.8, so the result from our seventh trial is 0. 77
4 This time there was one entry greater than 0.8, so the result from our eighth trial is 1. This time there were no entries greater than 0.8, so the result from our ninth trial is 0. This time there was one entry greater than 0.8, so the result from our tenth trial is 1. The sequence of results obtained is { 1, 0, 0, 0,1, 0, 0,1, 0,1 }. Using these results, we estimate the probabilities P( k ) for each k = 0,1, 2, 3, 4. Enter these estimates, as well as the exact values, in the table below. k Your Estimate of P(k) Actual Value of P(k) 6 0 = = = = = While the some of the estimates are not real close to the actual values, the biggest difference between actual and estimate is only Tossing a Loaded Coin Consider the experiment of tossing a loaded coin 8 times and counting the number of heads occurring in these 8 tosses. Simulate the experiment using a random number function on your calculator, considering a toss 78
5 to be tails (T) if the result is less than 0.80 and considering a toss to be heads (H) if the result is greater than or equal to Record the number of heads in 8 tosses. Repeat the experiment times, obtaining a sequence of numbers. Using these numbers, you can estimate the probability of 3 heads, P ( 3), by the ratio Number of times 3 appears in your sequence Calculate the actual probability using the binomial probability formula. How close is your estimate to the actual value? To simulate tossing the coin eight times, use rand(8). Store the results in the list L1, and go to the data editor under to view the results. Remember that we are using a random number generator, so your results will most likely differ from the results shown on the next page. Be sure to scroll down the list to see all the entries. There are two entries greater than 0.80, so our result for our first trial is 2. Return to the home screen and press Í to repeat the experiment again. 79
6 Again, there are two entries greater than 0.80, so the result from our second trial is 2. This time there was only one entry greater than 0.80, so the result from our third trial is 1. This time there were no entries greater than 0.80, so the result from our fourth trial is 0. This time there was one entry greater than 0.80, so the result from our fifth trial is 1. 80
7 This time there were three entries greater than 0.80, so the result from our sixth trial is 3. This time there were no entries greater than 0.8, so the result from our seventh trial is 0. This time there were two entries greater than 0.80, so the result from our eighth trial is 2. This time there were two entries greater than 0.80, so the result from our ninth trial is 2. 81
8 This time there was one entry greater than 0.80, so the result from our tenth trial is 1. The sequence of results obtained is { 2, 2,1, 0,1, 3, 0, 2, 2,1 }. There are two occurrences of 3 in the list, so the estimate of P ( 3) is 1 =. The exact value is P ( 3) = The estimate is fairly close to the actual value. 82
9 Summary No new commands were introduced in this chapter. 83
10 84
10-6 Study Guide and Intervention
10-6 Study Guide and Intervention Pascal s Triangle Pascal s triangle is the pattern of coefficients of powers of binomials displayed in triangular form. Each row begins and ends with 1 and each coefficient
More informationStatistics 6 th Edition
Statistics 6 th Edition Chapter 5 Discrete Probability Distributions Chap 5-1 Definitions Random Variables Random Variables Discrete Random Variable Continuous Random Variable Ch. 5 Ch. 6 Chap 5-2 Discrete
More informationBinomial and multinomial distribution
1-Binomial distribution Binomial and multinomial distribution The binomial probability refers to the probability that a binomial experiment results in exactly "x" successes. The probability of an event
More informationDecision Trees: Booths
DECISION ANALYSIS Decision Trees: Booths Terri Donovan recorded: January, 2010 Hi. Tony has given you a challenge of setting up a spreadsheet, so you can really understand whether it s wiser to play in
More informationBinomial Random Variables. Binomial Random Variables
Bernoulli Trials Definition A Bernoulli trial is a random experiment in which there are only two possible outcomes - success and failure. 1 Tossing a coin and considering heads as success and tails as
More informationStat 20: Intro to Probability and Statistics
Stat 20: Intro to Probability and Statistics Lecture 13: Binomial Formula Tessa L. Childers-Day UC Berkeley 14 July 2014 By the end of this lecture... You will be able to: Calculate the ways an event can
More informationWhat do you think "Binomial" involves?
Learning Goals: * Define a binomial experiment (Bernoulli Trials). * Applying the binomial formula to solve problems. * Determine the expected value of a Binomial Distribution What do you think "Binomial"
More informationLean Six Sigma: Training/Certification Books and Resources
Lean Si Sigma Training/Certification Books and Resources Samples from MINITAB BOOK Quality and Si Sigma Tools using MINITAB Statistical Software A complete Guide to Si Sigma DMAIC Tools using MINITAB Prof.
More informationChapter 3 - Lecture 5 The Binomial Probability Distribution
Chapter 3 - Lecture 5 The Binomial Probability October 12th, 2009 Experiment Examples Moments and moment generating function of a Binomial Random Variable Outline Experiment Examples A binomial experiment
More informationStat511 Additional Materials
Binomial Random Variable Stat511 Additional Materials The first discrete RV that we will discuss is the binomial random variable. The binomial random variable is a result of observing the outcomes from
More informationMath 166: Topics in Contemporary Mathematics II
Math 166: Topics in Contemporary Mathematics II Ruomeng Lan Texas A&M University October 15, 2014 Ruomeng Lan (TAMU) Math 166 October 15, 2014 1 / 12 Mean, Median and Mode Definition: 1. The average or
More informationExperimental Probability - probability measured by performing an experiment for a number of n trials and recording the number of outcomes
MDM 4U Probability Review Properties of Probability Experimental Probability - probability measured by performing an experiment for a number of n trials and recording the number of outcomes Theoretical
More informationStatistics for Managers Using Microsoft Excel 7 th Edition
Statistics for Managers Using Microsoft Excel 7 th Edition Chapter 5 Discrete Probability Distributions Statistics for Managers Using Microsoft Excel 7e Copyright 014 Pearson Education, Inc. Chap 5-1 Learning
More informationProbability and Statistics. Copyright Cengage Learning. All rights reserved.
Probability and Statistics Copyright Cengage Learning. All rights reserved. 14.3 Binomial Probability Copyright Cengage Learning. All rights reserved. Objectives Binomial Probability The Binomial Distribution
More informationChapter 5 Probability Distributions. Section 5-2 Random Variables. Random Variable Probability Distribution. Discrete and Continuous Random Variables
Chapter 5 Probability Distributions Section 5-2 Random Variables 5-2 Random Variables 5-3 Binomial Probability Distributions 5-4 Mean, Variance and Standard Deviation for the Binomial Distribution Random
More informationVIDEO 1. A random variable is a quantity whose value depends on chance, for example, the outcome when a die is rolled.
Part 1: Probability Distributions VIDEO 1 Name: 11-10 Probability and Binomial Distributions A random variable is a quantity whose value depends on chance, for example, the outcome when a die is rolled.
More informationBusiness Statistics 41000: Probability 4
Business Statistics 41000: Probability 4 Drew D. Creal University of Chicago, Booth School of Business February 14 and 15, 2014 1 Class information Drew D. Creal Email: dcreal@chicagobooth.edu Office:
More information5.4 Normal Approximation of the Binomial Distribution
5.4 Normal Approximation of the Binomial Distribution Bernoulli Trials have 3 properties: 1. Only two outcomes - PASS or FAIL 2. n identical trials Review from yesterday. 3. Trials are independent - probability
More informationWe use probability distributions to represent the distribution of a discrete random variable.
Now we focus on discrete random variables. We will look at these in general, including calculating the mean and standard deviation. Then we will look more in depth at binomial random variables which are
More informationExample 1: Identify the following random variables as discrete or continuous: a) Weight of a package. b) Number of students in a first-grade classroom
Section 5-1 Probability Distributions I. Random Variables A variable x is a if the value that it assumes, corresponding to the of an experiment, is a or event. A random variable is if it potentially can
More informationProbability Distributions
Chapter 6 Discrete Probability Distributions Section 6-2 Probability Distributions Definitions Let S be the sample space of a probability experiment. A random variable X is a function from the set S into
More informationThe binomial distribution p314
The binomial distribution p314 Example: A biased coin (P(H) = p = 0.6) ) is tossed 5 times. Let X be the number of H s. Fine P(X = 2). This X is a binomial r. v. The binomial setting p314 1. There are
More informationChapter 5. Sampling Distributions
Lecture notes, Lang Wu, UBC 1 Chapter 5. Sampling Distributions 5.1. Introduction In statistical inference, we attempt to estimate an unknown population characteristic, such as the population mean, µ,
More informationSection Random Variables
Section 6.2 - Random Variables According to the Bureau of the Census, the latest family data pertaining to family size for a small midwestern town, Nomore, is shown in Table 6.. If a family from this town
More informationChapter 6: Random Variables. Ch. 6-3: Binomial and Geometric Random Variables
Chapter : Random Variables Ch. -3: Binomial and Geometric Random Variables X 0 2 3 4 5 7 8 9 0 0 P(X) 3???????? 4 4 When the same chance process is repeated several times, we are often interested in whether
More informationEcon 6900: Statistical Problems. Instructor: Yogesh Uppal
Econ 6900: Statistical Problems Instructor: Yogesh Uppal Email: yuppal@ysu.edu Lecture Slides 4 Random Variables Probability Distributions Discrete Distributions Discrete Uniform Probability Distribution
More information23.1 Probability Distributions
3.1 Probability Distributions Essential Question: What is a probability distribution for a discrete random variable, and how can it be displayed? Explore Using Simulation to Obtain an Empirical Probability
More informationLecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 5 Probability Distributions 5-1 Overview 5-2 Random Variables 5-3 Binomial Probability
More information5.4 Normal Approximation of the Binomial Distribution Lesson MDM4U Jensen
5.4 Normal Approximation of the Binomial Distribution Lesson MDM4U Jensen Review From Yesterday Bernoulli Trials have 3 properties: 1. 2. 3. Binomial Probability Distribution In a binomial experiment with
More informationThe instructions on this page also work for the TI-83 Plus and the TI-83 Plus Silver Edition.
The instructions on this page also work for the TI-83 Plus and the TI-83 Plus Silver Edition. The position of the graphically represented keys can be found by moving your mouse on top of the graphic. Turn
More informationchapter 13: Binomial Distribution Exercises (binomial)13.6, 13.12, 13.22, 13.43
chapter 13: Binomial Distribution ch13-links binom-tossing-4-coins binom-coin-example ch13 image Exercises (binomial)13.6, 13.12, 13.22, 13.43 CHAPTER 13: Binomial Distributions The Basic Practice of Statistics
More informationChapter 3: Probability Distributions and Statistics
Chapter 3: Probability Distributions and Statistics Section 3.-3.3 3. Random Variables and Histograms A is a rule that assigns precisely one real number to each outcome of an experiment. We usually denote
More informationPart 10: The Binomial Distribution
Part 10: The Binomial Distribution The binomial distribution is an important example of a probability distribution for a discrete random variable. It has wide ranging applications. One readily available
More informationx is a random variable which is a numerical description of the outcome of an experiment.
Chapter 5 Discrete Probability Distributions Random Variables is a random variable which is a numerical description of the outcome of an eperiment. Discrete: If the possible values change by steps or jumps.
More informationConfidence Intervals and Sample Size
Confidence Intervals and Sample Size Chapter 6 shows us how we can use the Central Limit Theorem (CLT) to 1. estimate a population parameter (such as the mean or proportion) using a sample, and. determine
More informationProbability Models.S2 Discrete Random Variables
Probability Models.S2 Discrete Random Variables Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard Results of an experiment involving uncertainty are described by one or more random
More informationEssential Question: What is a probability distribution for a discrete random variable, and how can it be displayed?
COMMON CORE N 3 Locker LESSON Distributions Common Core Math Standards The student is expected to: COMMON CORE S-IC.A. Decide if a specified model is consistent with results from a given data-generating
More informationbinomial day 1.notebook December 10, 2013 Probability Quick Review of Probability Distributions!
Probability Binomial Distributions Day 1 Quick Review of Probability Distributions! # boys born in 4 births, x 0 1 2 3 4 Probability, P(x) 0.0625 0.25 0.375 0.25 0.0625 TWO REQUIREMENTS FOR A PROBABILITY
More informationthe number of correct answers on question i. (Note that the only possible values of X i
6851_ch08_137_153 16/9/02 19:48 Page 137 8 8.1 (a) No: There is no fixed n (i.e., there is no definite upper limit on the number of defects). (b) Yes: It is reasonable to believe that all responses are
More informationAP Statistics Ch 8 The Binomial and Geometric Distributions
Ch 8.1 The Binomial Distributions The Binomial Setting A situation where these four conditions are satisfied is called a binomial setting. 1. Each observation falls into one of just two categories, which
More informationBinomial distribution
Binomial distribution Jon Michael Gran Department of Biostatistics, UiO MF9130 Introductory course in statistics Tuesday 24.05.2010 1 / 28 Overview Binomial distribution (Aalen chapter 4, Kirkwood and
More informationChapter 8 Probability Models
Chapter 8 Probability Models We ve already used the calculator to find probabilities based on normal models. There are many more models which are useful. This chapter explores three such models. Many types
More informationDiscrete Probability Distributions
Page 1 of 6 Discrete Probability Distributions In order to study inferential statistics, we need to combine the concepts from descriptive statistics and probability. This combination makes up the basics
More informationThe Binomial Distribution
AQR Reading: Binomial Probability Reading #1: The Binomial Distribution A. It would be very tedious if, every time we had a slightly different problem, we had to determine the probability distributions
More informationGETTING STARTED. To OPEN MINITAB: Click Start>Programs>Minitab14>Minitab14 or Click Minitab 14 on your Desktop
Minitab 14 1 GETTING STARTED To OPEN MINITAB: Click Start>Programs>Minitab14>Minitab14 or Click Minitab 14 on your Desktop The Minitab session will come up like this 2 To SAVE FILE 1. Click File>Save Project
More informationThe Binomial distribution
The Binomial distribution Examples and Definition Binomial Model (an experiment ) 1 A series of n independent trials is conducted. 2 Each trial results in a binary outcome (one is labeled success the other
More informationThe Binomial Distribution
MATH 382 The Binomial Distribution Dr. Neal, WKU Suppose there is a fixed probability p of having an occurrence (or success ) on any single attempt, and a sequence of n independent attempts is made. Then
More informationProbability & Statistics Chapter 5: Binomial Distribution
Probability & Statistics Chapter 5: Binomial Distribution Notes and Examples Binomial Distribution When a variable can be viewed as having only two outcomes, call them success and failure, it may be considered
More informationExamples: Random Variables. Discrete and Continuous Random Variables. Probability Distributions
Random Variables Examples: Random variable a variable (typically represented by x) that takes a numerical value by chance. Number of boys in a randomly selected family with three children. Possible values:
More informationStatistical Methods in Practice STAT/MATH 3379
Statistical Methods in Practice STAT/MATH 3379 Dr. A. B. W. Manage Associate Professor of Mathematics & Statistics Department of Mathematics & Statistics Sam Houston State University Overview 6.1 Discrete
More informationMath 361. Day 8 Binomial Random Variables pages 27 and 28 Inv Do you have ESP? Inv. 1.3 Tim or Bob?
Math 361 Day 8 Binomial Random Variables pages 27 and 28 Inv. 1.2 - Do you have ESP? Inv. 1.3 Tim or Bob? Inv. 1.1: Friend or Foe Review Is a particular study result consistent with the null model? Learning
More informationx p(x)
You will work with your teacher on this activity. To begin open the activity and you will be greeted with the opening page. To read the entire introduction you will need to scroll down the page. Problem
More informationStatistics TI-83 Usage Handout
Statistics TI-83 Usage Handout This handout includes instructions for performing several different functions on a TI-83 calculator for use in Statistics. The Contents table below lists the topics covered
More informationLearning Objec0ves. Statistics for Business and Economics. Discrete Probability Distribu0ons
Statistics for Business and Economics Discrete Probability Distribu0ons Learning Objec0ves In this lecture, you learn: The proper0es of a probability distribu0on To compute the expected value and variance
More informationLAB 2 Random Variables, Sampling Distributions of Counts, and Normal Distributions
LAB 2 Random Variables, Sampling Distributions of Counts, and Normal Distributions The ECA 225 has open lab hours if you need to finish LAB 2. The lab is open Monday-Thursday 6:30-10:00pm and Saturday-Sunday
More informationChapter 5 Discrete Probability Distributions. Random Variables Discrete Probability Distributions Expected Value and Variance
Chapter 5 Discrete Probability Distributions Random Variables Discrete Probability Distributions Expected Value and Variance.40.30.20.10 0 1 2 3 4 Random Variables A random variable is a numerical description
More informationChapter 5 Discrete Probability Distributions Emu
CHAPTER 5 DISCRETE PROBABILITY DISTRIBUTIONS EMU PDF - Are you looking for chapter 5 discrete probability distributions emu Books? Now, you will be happy that at this time chapter 5 discrete probability
More informationECON 214 Elements of Statistics for Economists 2016/2017
ECON 214 Elements of Statistics for Economists 2016/2017 Topic Probability Distributions: Binomial and Poisson Distributions Lecturer: Dr. Bernardin Senadza, Dept. of Economics bsenadza@ug.edu.gh College
More informationS = 1,2,3, 4,5,6 occurs
Chapter 5 Discrete Probability Distributions The observations generated by different statistical experiments have the same general type of behavior. Discrete random variables associated with these experiments
More informationMA 1125 Lecture 12 - Mean and Standard Deviation for the Binomial Distribution. Objectives: Mean and standard deviation for the binomial distribution.
MA 5 Lecture - Mean and Standard Deviation for the Binomial Distribution Friday, September 9, 07 Objectives: Mean and standard deviation for the binomial distribution.. Mean and Standard Deviation of the
More informationChapter 3 Discrete Random Variables and Probability Distributions
Chapter 3 Discrete Random Variables and Probability Distributions Part 3: Special Discrete Random Variable Distributions Section 3.5 Discrete Uniform Section 3.6 Bernoulli and Binomial Others sections
More informationChapter 3. Discrete Probability Distributions
Chapter 3 Discrete Probability Distributions 1 Chapter 3 Overview Introduction 3-1 The Binomial Distribution 3-2 Other Types of Distributions 2 Chapter 3 Objectives Find the exact probability for X successes
More informationLecture 9: Plinko Probabilities, Part III Random Variables, Expected Values and Variances
Physical Principles in Biology Biology 3550 Fall 2018 Lecture 9: Plinko Probabilities, Part III Random Variables, Expected Values and Variances Monday, 10 September 2018 c David P. Goldenberg University
More informationguessing Bluman, Chapter 5 2
Bluman, Chapter 5 1 guessing Suppose there is multiple choice quiz on a subject you don t know anything about. 15 th Century Russian Literature; Nuclear physics etc. You have to guess on every question.
More informationMath Tech IIII, Apr 30
Math Tech IIII, Apr 30 The Binomial Distribution II Book Sections: 4.2 Essential Questions: How can I compute the probability of any event? What do I need to know about the binomial distribution? Besides
More informationThe binomial distribution
The binomial distribution The coin toss - three coins The coin toss - four coins The binomial probability distribution Rolling dice Using the TI nspire Graph of binomial distribution Mean & standard deviation
More informationThe Central Limit Theorem
The Central Limit Theorem Patrick Breheny March 1 Patrick Breheny University of Iowa Introduction to Biostatistics (BIOS 4120) 1 / 29 Kerrich s experiment Introduction The law of averages Mean and SD of
More informationThe Binomial Distribution
The Binomial Distribution January 31, 2018 Contents The Binomial Distribution The Normal Approximation to the Binomial The Binomial Hypothesis Test Computing Binomial Probabilities in R 30 Problems The
More informationProbability Models. Grab a copy of the notes on the table by the door
Grab a copy of the notes on the table by the door Bernoulli Trials Suppose a cereal manufacturer puts pictures of famous athletes in boxes of cereal, in the hope of increasing sales. The manufacturer announces
More informationTOPIC: PROBABILITY DISTRIBUTIONS
TOPIC: PROBABILITY DISTRIBUTIONS There are two types of random variables: A Discrete random variable can take on only specified, distinct values. A Continuous random variable can take on any value within
More informationThe Binomial Distribution
The Binomial Distribution January 31, 2019 Contents The Binomial Distribution The Normal Approximation to the Binomial The Binomial Hypothesis Test Computing Binomial Probabilities in R 30 Problems The
More informationCHAPTER 4 DISCRETE PROBABILITY DISTRIBUTIONS
CHAPTER 4 DISCRETE PROBABILITY DISTRIBUTIONS A random variable is the description of the outcome of an experiment in words. The verbal description of a random variable tells you how to find or calculate
More informationProbability Distributions: Discrete
Probability Distributions: Discrete INFO-2301: Quantitative Reasoning 2 Michael Paul and Jordan Boyd-Graber FEBRUARY 19, 2017 INFO-2301: Quantitative Reasoning 2 Paul and Boyd-Graber Probability Distributions:
More informationNormal Approximation to Binomial Distributions
Normal Approximation to Binomial Distributions Charlie Vollmer Department of Statistics Colorado State University Fort Collins, CO charlesv@rams.colostate.edu May 19, 2017 Abstract This document is a supplement
More informationThe Binomial Probability Distribution
The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2017 Objectives After this lesson we will be able to: determine whether a probability
More informationProbability Distributions for Discrete RV
Probability Distributions for Discrete RV Probability Distributions for Discrete RV Definition The probability distribution or probability mass function (pmf) of a discrete rv is defined for every number
More informationChapter 3 Discrete Random Variables and Probability Distributions
Chapter 3 Discrete Random Variables and Probability Distributions Part 4: Special Discrete Random Variable Distributions Sections 3.7 & 3.8 Geometric, Negative Binomial, Hypergeometric NOTE: The discrete
More informationMath Tech IIII, Mar 13
Math Tech IIII, Mar 13 The Binomial Distribution III Book Sections: 4.2 Essential Questions: What do I need to know about the binomial distribution? Standards: DA-5.6 What Makes a Binomial Experiment?
More informationSolutions for practice questions: Chapter 15, Probability Distributions If you find any errors, please let me know at
Solutions for practice questions: Chapter 15, Probability Distributions If you find any errors, please let me know at mailto:msfrisbie@pfrisbie.com. 1. Let X represent the savings of a resident; X ~ N(3000,
More informationBasics of Probability
Basics of Probability By A.V. Vedpuriswar October 2, 2016 2, 2016 Random variables and events A random variable is an uncertain quantity. A outcome is an observed value of a random variable. An event is
More informationSection 8.4 The Binomial Distribution
Section 8.4 The Binomial Distribution Binomial Experiment A binomial experiment has the following properties: 1. The number of trials in the experiment is fixed. 2. There are two outcomes of each trial:
More informationRandom Variables CHAPTER 6.3 BINOMIAL AND GEOMETRIC RANDOM VARIABLES
Random Variables CHAPTER 6.3 BINOMIAL AND GEOMETRIC RANDOM VARIABLES Essential Question How can I determine whether the conditions for using binomial random variables are met? Binomial Settings When the
More informationChapter 8: Binomial and Geometric Distributions
Chapter 8: Binomial and Geometric Distributions Section 8.1 Binomial Distributions The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Section 8.1 Binomial Distribution Learning Objectives
More informationPre-Calculus. Slide 1 / 145. Slide 2 / 145. Slide 3 / 145. Sequences and Series. Table of Contents
Slide 1 / 145 Pre-Calculus Slide 2 / 145 Sequences and Series 2015-03-24 www.njctl.org Table of Contents s Arithmetic Series Geometric Sequences Geometric Series Infinite Geometric Series Special Sequences
More information6.1 Binomial Theorem
Unit 6 Probability AFM Valentine 6.1 Binomial Theorem Objective: I will be able to read and evaluate binomial coefficients. I will be able to expand binomials using binomial theorem. Vocabulary Binomial
More informationChapter Five. The Binomial Probability Distribution and Related Topics
Chapter Five The Binomial Probability Distribution and Related Topics Section 3 Additional Properties of the Binomial Distribution Essential Questions How are the mean and standard deviation determined
More informationChapter 5 Basic Probability
Chapter 5 Basic Probability Probability is determining the probability that a particular event will occur. Probability of occurrence = / T where = the number of ways in which a particular event occurs
More informationChapter 6 Finance. 5.5 Annuities and Amortization Using Recursive Sequences
Chapter 6 Finance 5.5 Annuities and Amortization Using Recursive Sequences 3. Credit Card Debt John has a balance of $3000 on his credit card that charges 1% interest per month on any unpaid balance. John
More informationMA : Introductory Probability
MA 320-001: Introductory Probability David Murrugarra Department of Mathematics, University of Kentucky http://www.math.uky.edu/~dmu228/ma320/ Spring 2017 David Murrugarra (University of Kentucky) MA 320:
More informationLesson 97 - Binomial Distributions IBHL2 - SANTOWSKI
Lesson 97 - Binomial Distributions IBHL2 - SANTOWSKI Opening Exercise: Example #: (a) Use a tree diagram to answer the following: You throwing a bent coin 3 times where P(H) = / (b) THUS, find the probability
More informationOpening Exercise: Lesson 91 - Binomial Distributions IBHL2 - SANTOWSKI
08-0- Lesson 9 - Binomial Distributions IBHL - SANTOWSKI Opening Exercise: Example #: (a) Use a tree diagram to answer the following: You throwing a bent coin times where P(H) = / (b) THUS, find the probability
More information. Write the series, substituting the appropriate values for t 1. t 2. t 1. t 3
Geometric Series 2.3 A large telemarketing call centre will be closed on Monday due to an ice storm, and the employees are notified on Sunday. The company has already set up an emergency phone tree. The
More informationProbability Distribution Unit Review
Probability Distribution Unit Review Topics: Pascal's Triangle and Binomial Theorem Probability Distributions and Histograms Expected Values, Fair Games of chance Binomial Distributions Hypergeometric
More informationBinomial Distributions
Binomial Distributions (aka Bernouli s Trials) Chapter 8 Binomial Distribution an important class of probability distributions, which occur under the following Binomial Setting (1) There is a number n
More informationProbability Distributions: Discrete
Probability Distributions: Discrete Introduction to Data Science Algorithms Jordan Boyd-Graber and Michael Paul SEPTEMBER 27, 2016 Introduction to Data Science Algorithms Boyd-Graber and Paul Probability
More informationStatistics 431 Spring 2007 P. Shaman. Preliminaries
Statistics 4 Spring 007 P. Shaman The Binomial Distribution Preliminaries A binomial experiment is defined by the following conditions: A sequence of n trials is conducted, with each trial having two possible
More informationEx 1) Suppose a license plate can have any three letters followed by any four digits.
AFM Notes, Unit 1 Probability Name 1-1 FPC and Permutations Date Period ------------------------------------------------------------------------------------------------------- The Fundamental Principle
More informationEXERCISES ACTIVITY 6.7
762 CHAPTER 6 PROBABILITY MODELS EXERCISES ACTIVITY 6.7 1. Compute each of the following: 100! a. 5! I). 98! c. 9P 9 ~~ d. np 9 g- 8Q e. 10^4 6^4 " 285^1 f-, 2 c 5 ' sq ' sq 2. How many different ways
More informationCHAPTER 8 PROBABILITY DISTRIBUTIONS AND STATISTICS
CHAPTER 8 PROBABILITY DISTRIBUTIONS AND STATISTICS 8.1 Distribution of Random Variables Random Variable Probability Distribution of Random Variables 8.2 Expected Value Mean Mean is the average value of
More informationMATH1215: Mathematical Thinking Sec. 08 Spring Worksheet 9: Solution. x P(x)
N. Name: MATH: Mathematical Thinking Sec. 08 Spring 0 Worksheet 9: Solution Problem Compute the expected value of this probability distribution: x 3 8 0 3 P(x) 0. 0.0 0.3 0. Clearly, a value is missing
More information