Objective: To understand similarities and differences between geometric and binomial scenarios and to solve problems related to these scenarios.
|
|
|
- Jasmin Parks
- 5 years ago
- Views:
Transcription
1 AP Statistics: Geometric and Binomial Scenarios Objective: To understand similarities and differences between geometric and binomial scenarios and to solve problems related to these scenarios. Everything you need to know about Geometric and Binomial Models in 23 minutes: Porinchak, D. (2016, Dec. 14). APStatistics Binomial and Geometric Models --Youtube Common characteristics of Geometric and Binomial Scenarios (Bernoulli Trials) S I P Geometric Model Only concerned with. What is the probability I will my first success on x trial? P(X=x) = What is the expected number of trials I need to conduct before reaching my first success? µ = Standard Deviation: σ = Binomial Model How many successes will we get in n trials. We need. What is the probability we will get x successes in n trials? P(X=x) = where ( nn xx ) is the number of ways of finding x successes in n trials. What is the expected number of success that I will get in n trials? µ = Standard Deviation: σ = AP Stats Geometric and Binomial Scenarios 1
2 Quick Review of Combinations: The number of combinations is calculated when you have some number of trials (or options) and you want to choose x number out of the those options. Some ways of noting combinations: ( nn xx ) = nn! xx! nn xx! ncr -> read as n choose r For example, I have 5 books on my book shelf. I want to take 3 of those books with me on vacation. How many combinations of books can I take? ( 5 3 ) = 5! 3! 5 3! = 10 Ten combinations of 3 books out of 5 5C3 Chart it out: B1, B2, B3 B1, B2, B4 B1, B2, B5 B1, B3, B4 B1, B3, B5 B1, B4, B5 B2, B3, B4 B2, B3, B5 B2, B4, B5 B3, B4, B5 AP Stats Geometric and Binomial Scenarios 2
3 Geometric Example: Donating Blood People with O-negative blood are called universal donors because O- negative blood can be given to anyone else, regardless of the recipient s blood type. Only about 6% or the people have O-negative blood. Donor s line up at random for the blood drive. 1. Does this scenario meet the SIP criteria? Why or why not? Yes. S each person is either o-neg (success), or not (failure) I The blood type of one person does not affect the blood type of the next person in line. P the probability that any one person has o-neg blood is 6% 2. How many people do you expect to examine before you find someone who has O-negative blood? μ = 1 pp = What is the probability that the first O-negative donor found is one of the first four people in line? P(X 4) = P(X=1) + P(X+2) + P(X=3) + P(X=4) = (0.06) + (0.94)(0.06) (0.06) (0.06) AP Stats Geometric and Binomial Scenarios 3
4 Binomial Example: Donating Blood Same scenario. People with O-negative blood are called universal donors because O-negative blood can be given to anyone else, regardless of the recipient s blood type. Only about 6% or the people have O-negative blood. Donor s line up at random for the blood drive. 1. Suppose 20 donors come to the blood drive. What are the mean and standard deviation of the number of universal donors among them? This scenario still meets the SIP criteria and this scenario has a specific number of trials. We have n, and n=20. μ = np = (20)(0.06) =1.2, we expect 1.2 (people to have o-neg blood among n=20 people. σ= (npq) = (20)(0.06)(0.94) 1.06, so we may have between 0.14 people and 2.26 people with o-neg blood in n=20 people. 2. What is the probability that there are 2 or 3 universal donors? P(X = 2 or 3) = P(X=2) + P(X=3) =( 20 2 )(0.06)2 (0.94) 18 + ( 20 3 )(0.06)3 (0.94) AP Stats Geometric and Binomial Scenarios 4
5 Calculator tips Geometric models to find the probability of any individual outcome geometpdf(p,x) calculates finding the first success on the xth trial To find the sum of individual outcomes geometcdf(p,x) calculates finding the first success on or before the xth trial Binomial models to find the probability of any individual outcome binompdf(n,p,x) calculates the probability of finding exactly x number of successes in n trials To find the sum of individual outcomes binomcdf(n,p,x) calculates total probability of finding x or fewer number of successes in n trials Note: pdf is short for probability density function cdf is short for cumulative density function AP Stats Geometric and Binomial Scenarios 5
Chapter 17 Probability Models
Chapter 17 Probability Models Overview Key Concepts Know how to tell if a situation involves Bernoulli trials. Be able to choose whether to use a Geometric or a Binomial model for a random variable involving
Probability 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
AP Statistics Quiz A Chapter 17
AP Statistics Quiz A Chapter 17 Name The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. 1. How many blood donors should the
Binomial Distribution. Normal Approximation to the Binomial
Binomial Distribution Normal Approximation to the Binomial /29 Homework Read Sec 6-6. Discussion Question pg 337 Do Ex 6-6 -4 2 /29 Objectives Objective: Use the normal approximation to calculate 3 /29
AP 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
MA : 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:
CIVL Discrete Distributions
CIVL 3103 Discrete Distributions Learning Objectives Define discrete distributions, and identify common distributions applicable to engineering problems. Identify the appropriate distribution (i.e. binomial,
Lecture 23. STAT 225 Introduction to Probability Models April 4, Whitney Huang Purdue University. Normal approximation to Binomial
Lecture 23 STAT 225 Introduction to Probability Models April 4, 2014 approximation Whitney Huang Purdue University 23.1 Agenda 1 approximation 2 approximation 23.2 Characteristics of the random variable:
Section 7.5 The Normal Distribution. Section 7.6 Application of the Normal Distribution
Section 7.6 Application of the Normal Distribution A random variable that may take on infinitely many values is called a continuous random variable. A continuous probability distribution is defined by
Chapter 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
No, because np = 100(0.02) = 2. The value of np must be greater than or equal to 5 to use the normal approximation.
1) If n 100 and p 0.02 in a binomial experiment, does this satisfy the rule for a normal approximation? Why or why not? No, because np 100(0.02) 2. The value of np must be greater than or equal to 5 to
Chapter 8: The Binomial and Geometric Distributions
Chapter 8: The Binomial and Geometric Distributions 8.1 Binomial Distributions 8.2 Geometric Distributions 1 Let me begin with an example My best friends from Kent School had three daughters. What is the
Binomial Distributions
Binomial Distributions Binomial Experiment The experiment is repeated for a fixed number of trials, where each trial is independent of the other trials There are only two possible outcomes of interest
Chpt The Binomial Distribution
Chpt 5 5-4 The Binomial Distribution 1 /36 Chpt 5-4 Chpt 5 Homework p262 Applying the Concepts Exercises p263 1-11, 14-18, 23, 24, 26 2 /36 Objective Chpt 5 Find the exact probability for x successes in
Probability Theory. Mohamed I. Riffi. Islamic University of Gaza
Probability Theory Mohamed I. Riffi Islamic University of Gaza Table of contents 1. Chapter 2 Discrete Distributions The binomial distribution 1 Chapter 2 Discrete Distributions Bernoulli trials and the
The Binomial and Geometric Distributions. Chapter 8
The Binomial and Geometric Distributions Chapter 8 8.1 The Binomial Distribution A binomial experiment is statistical experiment that has the following properties: The experiment consists of n repeated
The 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
Discrete Probability Distribution
1 Discrete Probability Distribution Key Definitions Discrete Random Variable: Has a countable number of values. This means that each data point is distinct and separate. Continuous Random Variable: Has
STA258H5. Al Nosedal and Alison Weir. Winter Al Nosedal and Alison Weir STA258H5 Winter / 41
STA258H5 Al Nosedal and Alison Weir Winter 2017 Al Nosedal and Alison Weir STA258H5 Winter 2017 1 / 41 NORMAL APPROXIMATION TO THE BINOMIAL DISTRIBUTION. Al Nosedal and Alison Weir STA258H5 Winter 2017
PROBABILITY DISTRIBUTIONS. Chapter 6
PROBABILITY DISTRIBUTIONS Chapter 6 6.1 Summarize Possible Outcomes and their Probabilities Random Variable Random variable is numerical outcome of random phenomenon www.physics.umd.edu 3 Random Variable
Probability is the tool used for anticipating what the distribution of data should look like under a given model.
AP Statistics NAME: Exam Review: Strand 3: Anticipating Patterns Date: Block: III. Anticipating Patterns: Exploring random phenomena using probability and simulation (20%-30%) Probability is the tool used
Version A. Problem 1. Let X be the continuous random variable defined by the following pdf: 1 x/2 when 0 x 2, f(x) = 0 otherwise.
Math 224 Q Exam 3A Fall 217 Tues Dec 12 Version A Problem 1. Let X be the continuous random variable defined by the following pdf: { 1 x/2 when x 2, f(x) otherwise. (a) Compute the mean µ E[X]. E[X] x
Math 14 Lecture Notes Ch The Normal Approximation to the Binomial Distribution. P (X ) = nc X p X q n X =
6.4 The Normal Approximation to the Binomial Distribution Recall from section 6.4 that g A binomial experiment is a experiment that satisfies the following four requirements: 1. Each trial can have only
Lecture 8. The Binomial Distribution. Binomial Distribution. Binomial Distribution. Probability Distributions: Normal and Binomial
Lecture 8 The Binomial Distribution Probability Distributions: Normal and Binomial 1 2 Binomial Distribution >A binomial experiment possesses the following properties. The experiment consists of a fixed
Stat511 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
Math 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?
PROBABILITY AND STATISTICS CHAPTER 4 NOTES DISCRETE PROBABILITY DISTRIBUTIONS
PROBABILITY AND STATISTICS CHAPTER 4 NOTES DISCRETE PROBABILITY DISTRIBUTIONS I. INTRODUCTION TO RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS A. Random Variables 1. A random variable x represents a value
Discrete Probability Distributions and application in Business
http://wiki.stat.ucla.edu/socr/index.php/socr_courses_2008_thomson_econ261 Discrete Probability Distributions and application in Business By Grace Thomson DISCRETE PROBALITY DISTRIBUTIONS Discrete Probabilities
Chapter 14 - Random Variables
Chapter 14 - Random Variables October 29, 2014 There are many scenarios where probabilities are used to determine risk factors. Examples include Insurance, Casino, Lottery, Business, Medical, and other
AP STATISTICS FALL SEMESTSER FINAL EXAM STUDY GUIDE
AP STATISTICS Name: FALL SEMESTSER FINAL EXAM STUDY GUIDE Period: *Go over Vocabulary Notecards! *This is not a comprehensive review you still should look over your past notes, homework/practice, Quizzes,
Probability Theory and Simulation Methods. April 9th, Lecture 20: Special distributions
April 9th, 2018 Lecture 20: Special distributions Week 1 Chapter 1: Axioms of probability Week 2 Chapter 3: Conditional probability and independence Week 4 Chapters 4, 6: Random variables Week 9 Chapter
CVE SOME DISCRETE PROBABILITY DISTRIBUTIONS
CVE 472 2. SOME DISCRETE PROBABILITY DISTRIBUTIONS Assist. Prof. Dr. Bertuğ Akıntuğ Civil Engineering Program Middle East Technical University Northern Cyprus Campus CVE 472 Statistical Techniques in Hydrology.
Chapter 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
CH 5 Normal Probability Distributions Properties of the Normal Distribution
Properties of the Normal Distribution Example A friend that is always late. Let X represent the amount of minutes that pass from the moment you are suppose to meet your friend until the moment your friend
Binomial formulas: The binomial coefficient is the number of ways of arranging k successes among n observations.
Chapter 8 Notes Binomial and Geometric Distribution Often times we are interested in an event that has only two outcomes. For example, we may wish to know the outcome of a free throw shot (good or missed),
Math Tech IIII, Mar 6
Math Tech IIII, Mar 6 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? Standards:
Chapter 5: Probability models
Chapter 5: Probability models 1. Random variables: a) Idea. b) Discrete and continuous variables. c) The probability function (density) and the distribution function. d) Mean and variance of a random variable.
Week 7. Texas A& M University. Department of Mathematics Texas A& M University, College Station Section 3.2, 3.3 and 3.4
Week 7 Oğuz Gezmiş Texas A& M University Department of Mathematics Texas A& M University, College Station Section 3.2, 3.3 and 3.4 Oğuz Gezmiş (TAMU) Topics in Contemporary Mathematics II Week7 1 / 19
8.1 Binomial Situations
8.1 Binomial Situations "Dumb Dora" didn't study for her final exam. It was a true/false test, so she decided to flip a coin for the answers. The statistics professor watched her the entire two hours as
Binomial 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
8.1 Binomial Distributions
8.1 Binomial Distributions The Binomial Setting The 4 Conditions of a Binomial Setting: 1.Each observation falls into 1 of 2 categories ( success or fail ) 2 2.There is a fixed # n of observations. 3.All
The Normal Probability Distribution
1 The Normal Probability Distribution Key Definitions Probability Density Function: An equation used to compute probabilities for continuous random variables where the output value is greater than zero
Normal Distribution. Notes. Normal Distribution. Standard Normal. Sums of Normal Random Variables. Normal. approximation of Binomial.
Lecture 21,22, 23 Text: A Course in Probability by Weiss 8.5 STAT 225 Introduction to Probability Models March 31, 2014 Standard Sums of Whitney Huang Purdue University 21,22, 23.1 Agenda 1 2 Standard
UQ, STAT2201, 2017, Lectures 3 and 4 Unit 3 Probability Distributions.
UQ, STAT2201, 2017, Lectures 3 and 4 Unit 3 Probability Distributions. Random Variables 2 A random variable X is a numerical (integer, real, complex, vector etc.) summary of the outcome of the random experiment.
Random 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
Binomial 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
Probability Distributions. Definitions Discrete vs. Continuous Mean and Standard Deviation TI 83/84 Calculator Binomial Distribution
Probability Distributions Definitions Discrete vs. Continuous Mean and Standard Deviation TI 83/84 Calculator Binomial Distribution Definitions Random Variable: a variable that has a single numerical value
Discrete Random Variables and Probability Distributions. Stat 4570/5570 Based on Devore s book (Ed 8)
3 Discrete Random Variables and Probability Distributions Stat 4570/5570 Based on Devore s book (Ed 8) Random Variables We can associate each single outcome of an experiment with a real number: We refer
What is the probability of success? Failure? How could we do this simulation using a random number table?
Probability Ch.4, sections 4.2 & 4.3 Binomial and Geometric Distributions Name: Date: Pd: 4.2. What is a binomial distribution? How do we find the probability of success? Suppose you have three daughters.
CIVL Learning Objectives. Definitions. Discrete Distributions
CIVL 3103 Discrete Distributions Learning Objectives Define discrete distributions, and identify common distributions applicable to engineering problems. Identify the appropriate distribution (i.e. binomial,
4 Random Variables and Distributions
4 Random Variables and Distributions Random variables A random variable assigns each outcome in a sample space. e.g. called a realization of that variable to Note: We ll usually denote a random variable
When the observations of a quantitative random variable can take on only a finite number of values, or a countable number of values.
5.1 Introduction to Random Variables and Probability Distributions Statistical Experiment - any process by which an observation (or measurement) is obtained. Examples: 1) Counting the number of eggs in
Section 6.3 Binomial and Geometric Random Variables
Section 6.3 Binomial and Geometric Random Variables Mrs. Daniel AP Stats Binomial Settings A binomial setting arises when we perform several independent trials of the same chance process and record the
Section Introduction to Normal Distributions
Section 6.1-6.2 Introduction to Normal Distributions 2012 Pearson Education, Inc. All rights reserved. 1 of 105 Section 6.1-6.2 Objectives Interpret graphs of normal probability distributions Find areas
STAT Chapter 5: Continuous Distributions. Probability distributions are used a bit differently for continuous r.v. s than for discrete r.v. s.
STAT 515 -- Chapter 5: Continuous Distributions Probability distributions are used a bit differently for continuous r.v. s than for discrete r.v. s. Continuous distributions typically are represented by
2) There is a fixed number of observations n. 3) The n observations are all independent
Chapter 8 Binomial and Geometric Distributions The binomial setting consists of the following 4 characteristics: 1) Each observation falls into one of two categories success or failure 2) There is a fixed
7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4
7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4 - Would the correlation between x and y in the table above be positive or negative? The correlation is negative. -
The Central Limit Theorem. Sec. 8.2: The Random Variable. it s Distribution. it s Distribution
The Central Limit Theorem Sec. 8.1: The Random Variable it s Distribution Sec. 8.2: The Random Variable it s Distribution X p and and How Should You Think of a Random Variable? Imagine a bag with numbers
Probability Notes: Binomial Probabilities
Probability Notes: Binomial Probabilities A Binomial Probability is a type of discrete probability with only two outcomes (tea or coffee, win or lose, have disease or don t have disease). The category
Econ 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
Discrete Probability Distributions
Chapter 5 Discrete Probability Distributions Goal: To become familiar with how to use Excel 2007/2010 for binomial distributions. Instructions: Open Excel and click on the Stat button in the Quick Access
Chapter 8. Binomial and Geometric Distributions
Chapter 8 Binomial and Geometric Distributions Lesson 8-1, Part 1 Binomial Distribution What is a Binomial Distribution? Specific type of discrete probability distribution The outcomes belong to two categories
30 Wyner Statistics Fall 2013
30 Wyner Statistics Fall 2013 CHAPTER FIVE: DISCRETE PROBABILITY DISTRIBUTIONS Summary, Terms, and Objectives A probability distribution shows the likelihood of each possible outcome. This chapter deals
Probability 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
Using the Central Limit Theorem It is important for you to understand when to use the CLT. If you are being asked to find the probability of the
Using the Central Limit Theorem It is important for you to understand when to use the CLT. If you are being asked to find the probability of the mean, use the CLT for the mean. If you are being asked to
Midterm Test 1 (Sample) Student Name (PRINT):... Student Signature:... Use pencil, so that you can erase and rewrite if necessary.
MA 180/418 Midterm Test 1 (Sample) Student Name (PRINT):............................................. Student Signature:................................................... Use pencil, so that you can erase
Chapter 8. Variables. Copyright 2004 Brooks/Cole, a division of Thomson Learning, Inc.
Chapter 8 Random Variables Copyright 2004 Brooks/Cole, a division of Thomson Learning, Inc. 8.1 What is a Random Variable? Random Variable: assigns a number to each outcome of a random circumstance, or,
Chapter 6: Random Variables
Chapter 6: Random Variables Section 6.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 6 Random Variables 6.1 Discrete and Continuous Random Variables 6.2 Transforming and
chapter 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
Mathacle. PSet Stats, Concepts In Statistics Level Number Name: Date: Distribution Distribute in anyway but normal
Distribution Distribute in anyway but normal VI. DISTRIBUTION A probability distribution is a mathematical function that provides the probabilities of occurrence of all distinct outcomes in the sample
5.4 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
5.4 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
Chapter 7 1. Random Variables
Chapter 7 1 Random Variables random variable numerical variable whose value depends on the outcome of a chance experiment - discrete if its possible values are isolated points on a number line - continuous
guessing 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.
Engineering Statistics ECIV 2305
Engineering Statistics ECIV 2305 Section 5.3 Approximating Distributions with the Normal Distribution Introduction A very useful property of the normal distribution is that it provides good approximations
Chapter 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
Chapter 8 Solutions Page 1 of 15 CHAPTER 8 EXERCISE SOLUTIONS
Chapter 8 Solutions Page of 5 8. a. Continuous. b. Discrete. c. Continuous. d. Discrete. e. Discrete. 8. a. Discrete. b. Continuous. c. Discrete. d. Discrete. CHAPTER 8 EXERCISE SOLUTIONS 8.3 a. 3/6 =
Examples: 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:
II - Probability. Counting Techniques. three rules of counting. 1multiplication rules. 2permutations. 3combinations
II - Probability Counting Techniques three rules of counting 1multiplication rules 2permutations 3combinations Section 2 - Probability (1) II - Probability Counting Techniques 1multiplication rules In
Random Variables. Chapter 6: Random Variables 2/2/2014. Discrete and Continuous Random Variables. Transforming and Combining Random Variables
Chapter 6: Random Variables Section 6.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Random Variables 6.1 6.2 6.3 Discrete and Continuous Random Variables Transforming and Combining
Chapter 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
Discrete Random Variables and Their Probability Distributions
Chapter 5 Discrete Random Variables and Their Probability Distributions Mean and Standard Deviation of a Discrete Random Variable Computing the mean and standard deviation of a discrete random variable
Binomial and Geometric Distributions
Binomial and Geometric Distributions Section 3.2 & 3.3 Cathy Poliak, Ph.D. cathy@math.uh.edu Office hours: T Th 2:30 pm - 5:15 pm 620 PGH Department of Mathematics University of Houston February 11, 2016
4.2 Bernoulli Trials and Binomial Distributions
Arkansas Tech University MATH 3513: Applied Statistics I Dr. Marcel B. Finan 4.2 Bernoulli Trials and Binomial Distributions A Bernoulli trial 1 is an experiment with exactly two outcomes: Success and
Section 5 3 The Mean and Standard Deviation of a Binomial Distribution!
Section 5 3 The Mean and Standard Deviation of a Binomial Distribution! Previous sections required that you to find the Mean and Standard Deviation of a Binomial Distribution by using the values from a
Chapter 17. Probability Models. Copyright 2010 Pearson Education, Inc.
Chapter 17 Probability Models Copyright 2010 Pearson Education, Inc. Bernoulli Trials The basis for the probability models we will examine in this chapter is the Bernoulli trial. We have Bernoulli trials
Inverse Normal Distribution and Approximation to Binomial
Inverse Normal Distribution and Approximation to Binomial Section 5.5 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 16-3339 Cathy Poliak,
MidTerm 1) Find the following (round off to one decimal place):
MidTerm 1) 68 49 21 55 57 61 70 42 59 50 66 99 Find the following (round off to one decimal place): Mean = 58:083, round off to 58.1 Median = 58 Range = max min = 99 21 = 78 St. Deviation = s = 8:535,
Statistics 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
CHAPTER 6 Random Variables
CHAPTER 6 Random Variables 6.3 Binomial and Geometric Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Binomial and Geometric Random
Chapter 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
Binomial Random Variables. Binomial Distribution. Examples of Binomial Random Variables. Binomial Random Variables
Binomial Random Variables Binomial Distribution STAT Tom Ilvento In many cases the responses to an experiment are dichotomous Yes/No Alive/Dead Support/Don t Support Binomial Random Variables When our
Probability Distributions II
Probability Distributions II Summer 2017 Summer Institutes 63 Multinomial Distribution - Motivation Suppose we modified assumption (1) of the binomial distribution to allow for more than two outcomes.
CHAPTER 5 SOME DISCRETE PROBABILITY DISTRIBUTIONS. 5.2 Binomial Distributions. 5.1 Uniform Discrete Distribution
CHAPTER 5 SOME DISCRETE PROBABILITY DISTRIBUTIONS As we had discussed, there are two main types of random variables, namely, discrete random variables and continuous random variables. In this chapter,
Converting to the Standard Normal rv: Exponential PDF and CDF for x 0 Chapter 7: expected value of x
Key Formula Sheet ASU ECN 22 ASWCC Chapter : no key formulas Chapter 2: Relative Frequency=freq of the class/n Approx Class Width: =(largest value-smallest value) /number of classes Chapter 3: sample and
. 13. The maximum error (margin of error) of the estimate for μ (based on known σ) is:
Statistics Sample Exam 3 Solution Chapters 6 & 7: Normal Probability Distributions & Estimates 1. What percent of normally distributed data value lie within 2 standard deviations to either side of the
Lecture 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
6.4 approximating binomial distr with normal curve.notebook January 26, compute the mean/ expected value for the above distribution.
Discrete: Countable (no fractions or decimals) Continuous: Measurable: distance, time, volume Binomial Distribution n = number of trials r = number of successes p = probability of success q = probability
Chapter 11. Data Descriptions and Probability Distributions. Section 4 Bernoulli Trials and Binomial Distribution
Chapter 11 Data Descriptions and Probability Distributions Section 4 Bernoulli Trials and Binomial Distribution 1 Learning Objectives for Section 11.4 Bernoulli Trials and Binomial Distributions The student
Chapter. Section 4.2. Chapter 4. Larson/Farber 5 th ed 1. Chapter Outline. Discrete Probability Distributions. Section 4.
Chapter Discrete Probability s Chapter Outline 1 Probability s 2 Binomial s 3 More Discrete Probability s Copyright 2015, 2012, and 2009 Pearson Education, Inc 1 Copyright 2015, 2012, and 2009 Pearson