AP Statistics Ch 8 The Binomial and Geometric Distributions
|
|
- Cassandra McKenzie
- 6 years ago
- Views:
Transcription
1 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 we call success or failure. 2. There is a fixed number of n observations. 3. The n observations are all independent. 4. The probability of success, call it p, is the same for each observation. If data are produced in a binomial setting, then the random variable X = # of successes is called a binomial random variable. The probability distribution of X is called a binomial distribution. The distribution of the count X of successes in the binomial setting is the binomial distribution with parameters n and p. Abbreviated, we say X is B(n, p). The parameter n is the number of observations, and p is the probability of a success on any one observation. The possible values of X are the whole numbers from 0 to n. Example Binomial Setting o Indicate whether a binomial distribution is a reasonable model for the random variable X. Give your reasons in each case. o A manufacturer produces a large number of toasters. From past experience, the manufacturer knows that approximately 2% are defective. In a quality control procedure, we randomly select 20 toasters for testing. We want to determine the probability that no more than one of these toasters is defective. o Draw a card from a standard deck of 52 playing cards, observe the card, and replace the card within the deck. Count the number of times you draw a card in this manner until you observe a jack. page 1
2 Finding Binomial Probabilities Given a discrete random variable X, the probability distribution function (pdf) assigns a probability to each value of X. The command binompdf(n, p, X) calculates the binomial probability of value X. Given a random variable X, the cumulative distribution function (cdf) of X calculates the sum of the probabilities for 0, 1, 2,, up to the value X. That is, it calculates the probability of obtaining at most X successes in n trials. The command binomcdf(n, p, X) calculates the binomial probability that the variable takes on the values of 0 up to (and including) X. Example Flipping a Coin o A fair coin is flipped 6 times. o Determine the probability that the coin comes up tails exactly 5 times. o Find the probability that the coin comes up tails at least 1 time. o Find the probability that the coin comes up tails at most 3 times. o Construct a pdf table and a pdf histogram for the variable X. o Construct a cdf table and a cdf histogram for the variable X. page 2
3 Binomial Formulas For any positive whole number n, its factorial n! is n! = n (n 1) (n 2) and 0! = 1 The number of ways of arranging k successes among n observations is given by the binomial coefficient n n! = k k!(n k)! Say binomial coefficient n choose k. Calculator: MATH PRB ncr If X is B(n, p), the possible values of X are 0, 1, 2,, n. If k is any one of these values, P(X = k) = n p k (1 p) n k k Example Flipping a Coin o A fair coin is flipped 6 times. o Determine the probability that the coin comes up tails exactly 5 times. o Find the probability that the coin comes up tails at least 1 time. page 3
4 Binomial Mean and Standard Deviation If X is B(n, p), then the mean is μ = np and the standard deviation is σ = np(1 p) As the number of trials n gets larger, the binomial distribution gets close to a normal distribution. When n is large, we can use normal probability calculations to approximate hard-to-calculate binomial probabilities. As a rule of thumb, use the normal approximation when n and p and q satisfy np 10 and nq 10. (note: q is equal to 1 p) The accuracy of the normal approximation improves as the sample size n increases. It is most accurate for any fixed n when p is close to ½ and least accurate when p is near 0 or 1. Example IRS o The Internal Revenue Service estimates that 8% of all taxpayers filling out long forms make mistakes. Suppose that a random sample of 10,000 forms is selected. What is the approximate probability that more than 800 forms have mistakes? page 4
5 Ch 8.2 The Geometric Distributions The Geometric Setting A situation where these four conditions are satisfied is called a geometric setting. 1. Each observation falls into one of just two categories, which we call success or failure. 2. The probability of success, call it p, is the same for each observation. 3. The observations are all independent. 4. The variable of interest is the number of trials required to obtain the first success. If X has a geometric distribution with probability p of success and (1-p) of failure on each observation, the possible values of X are 1, 2, 3,. If n is any one of these values, the probability that the first success occurs on the nth trial is P(X = n) = (1 p) n 1 p The probability that it takes more than n trials to see the first success is P(X > n) = (1 p) n The mean, or expected value, of X is μ =1/ p. Example Overweight Americans o A survey conducted by the Harris polling organization discovered that 80% of all Americans are overweight. Suppose that a number of randomly selected Americans are weighed. o How many Americans would you expect to weigh before you encounter the first overweight individual? o Find the probability that the fourth person weighed is the first person to be overweight. o Find the probability that it takes more than 4 people to observe the first overweight person. page 1
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
More informationChapter 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
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 information***SECTION 8.1*** The Binomial Distributions
***SECTION 8.1*** The Binomial Distributions CHAPTER 8 ~ The Binomial and Geometric Distributions In practice, we frequently encounter random phenomenon where there are two outcomes of interest. For example,
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 informationChapter 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
More information30 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
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 informationBinomial and Normal Distributions. Example: Determine whether the following experiments are binomial experiments. Explain.
Binomial and Normal Distributions Objective 1: Determining if an Experiment is a Binomial Experiment For an experiment to be considered a binomial experiment, four things must hold: 1. The experiment is
More informationThe 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
More information6.3: The Binomial Model
6.3: The Binomial Model The Normal distribution is a good model for many situations involving a continuous random variable. For experiments involving a discrete random variable, where the outcome of the
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 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 informationName Period AP Statistics Unit 5 Review
Name Period AP Statistics Unit 5 Review Multiple Choice 1. Jay Olshansky from the University of Chicago was quoted in Chance News as arguing that for the average life expectancy to reach 100, 18% of people
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 informationDiscrete 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
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 information4.2 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
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 informationBinomal and Geometric Distributions
Binomal and Geometric Distributions Sections 3.2 & 3.3 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 7-2311 Cathy Poliak, Ph.D. cathy@math.uh.edu
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 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 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 informationMATH 264 Problem Homework I
MATH Problem Homework I Due to December 9, 00@:0 PROBLEMS & SOLUTIONS. A student answers a multiple-choice examination question that offers four possible answers. Suppose that the probability that 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 informationCHAPTER 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
More informationBinomial 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
More information3. The n observations are independent. Knowing the result of one observation tells you nothing about the other observations.
Binomial and Geometric Distributions - Terms and Formulas Binomial Experiments - experiments having all four conditions: 1. Each observation falls into one of two categories we call them success or failure.
More informationBinomial 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),
More information3. The n observations are independent. Knowing the result of one observation tells you nothing about the other observations.
Binomial and Geometric Distributions - Terms and Formulas Binomial Experiments - experiments having all four conditions: 1. Each observation falls into one of two categories we call them success or failure.
More informationChapter 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
More informationCHAPTER 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
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 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 informationObjective: To understand similarities and differences between geometric and binomial scenarios and to solve problems related to these scenarios.
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
More informationBinomial Probabilities The actual probability that P ( X k ) the formula n P X k p p. = for any k in the range {0, 1, 2,, n} is given by. n n!
Introduction We are often more interested in experiments in which there are two outcomes of interest (success/failure, make/miss, yes/no, etc.). In this chapter we study two types of probability distributions
More informationSampling Distributions For Counts and Proportions
Sampling Distributions For Counts and Proportions IPS Chapter 5.1 2009 W. H. Freeman and Company Objectives (IPS Chapter 5.1) Sampling distributions for counts and proportions Binomial distributions for
More informationProbability 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
More informationChapter 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
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 informationChapter 12. Binomial Setting. Binomial Setting Examples
Chapter 12 Binomial Distributions BPS - 3rd Ed. Chapter 12 1 Binomial Setting Fixed number n of observations The n observations are independent Each observation falls into one of just two categories may
More informationProbability 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
More informationVersion 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
More informationDiscrete 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
More informationWhat 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.
More informationCHAPTER 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 6.3 Reading Quiz (T or F) 1.
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 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
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 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
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 informationSection 8.4 The Binomial Distribution. (a) Rolling a fair die 20 times and observing how many heads appear. s
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 informationLecture 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:
More informationChapter 4 and 5 Note Guide: Probability Distributions
Chapter 4 and 5 Note Guide: Probability Distributions Probability Distributions for a Discrete Random Variable A discrete probability distribution function has two characteristics: Each probability is
More informationOverview. Definitions. Definitions. Graphs. Chapter 5 Probability Distributions. probability distributions
Chapter 5 Probability Distributions 5-1 Overview 5-2 Random Variables 5-3 Binomial Probability Distributions 5-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 5-5 The Poisson Distribution
More informationChapter 6 Section 3: Binomial and Geometric Random Variables
Name: Date: Period: Chapter 6 Section 3: Binomial and Geometric Random Variables When the same chance process is repeated several times, we are often interested whether a particular outcome does or does
More informationSection 8.4 The Binomial Distribution
Section 84 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: success
More information5.2 Random Variables, Probability Histograms and Probability Distributions
Chapter 5 5.2 Random Variables, Probability Histograms and Probability Distributions A random variable (r.v.) can be either continuous or discrete. It takes on the possible values of an experiment. It
More informationSome Discrete Distribution Families
Some Discrete Distribution Families ST 370 Many families of discrete distributions have been studied; we shall discuss the ones that are most commonly found in applications. In each family, we need a formula
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 informationNo, 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
More informationII - 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
More informationAP Statistics Review Ch. 6
AP Statistics Review Ch. 6 Name 1. Which of the following data sets is not continuous? a. The gallons of gasoline in a car. b. The time it takes to commute in a car. c. Number of goals scored by a hockey
More information15.063: Communicating with Data Summer Recitation 3 Probability II
15.063: Communicating with Data Summer 2003 Recitation 3 Probability II Today s Goal Binomial Random Variables (RV) Covariance and Correlation Sums of RV Normal RV 15.063, Summer '03 2 Random Variables
More information8.1 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
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 information***SECTION 7.1*** Discrete and Continuous Random Variables
***SECTION 7.1*** Discrete and Continuous Random Variables UNIT 6 ~ Random Variables Sample spaces need not consist of numbers; tossing coins yields H s and T s. However, in statistics we are most often
More informationSection 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
More informationChapter 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
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 informationRandom 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
More informationX P(X) (c) Express the event performing at least two tests in terms of X and find its probability.
AP Stats ~ QUIZ 6 Name Period 1. The probability distribution below is for the random variable X = number of medical tests performed on a randomly selected outpatient at a certain hospital. X 0 1 2 3 4
More information8.1 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
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 informationUsing 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
More informationA random variable (r. v.) is a variable whose value is a numerical outcome of a random phenomenon.
Chapter 14: random variables p394 A random variable (r. v.) is a variable whose value is a numerical outcome of a random phenomenon. Consider the experiment of tossing a coin. Define a random variable
More informationBinomial Random Variable - The count X of successes in a binomial setting
6.3.1 Binomial Settings and Binomial Random Variables What do the following scenarios have in common? Toss a coin 5 times. Count the number of heads. Spin a roulette wheel 8 times. Record how many times
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 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 information. 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
More informationNormal distribution Approximating binomial distribution by normal 2.10 Central Limit Theorem
1.1.2 Normal distribution 1.1.3 Approimating binomial distribution by normal 2.1 Central Limit Theorem Prof. Tesler Math 283 Fall 216 Prof. Tesler 1.1.2-3, 2.1 Normal distribution Math 283 / Fall 216 1
More informationAMS 7 Sampling Distributions, Central limit theorem, Confidence Intervals Lecture 4
AMS 7 Sampling Distributions, Central limit theorem, Confidence Intervals Lecture 4 Department of Applied Mathematics and Statistics, University of California, Santa Cruz Summer 2014 1 / 26 Sampling Distributions!!!!!!
More information2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 4 Random Variables & Probability Distributions Content 1. Two Types of Random Variables 2. Probability Distributions for Discrete Random Variables 3. The Binomial
More informationStatistics Chapter 8
Statistics Chapter 8 Binomial & Geometric Distributions Time: 1.5 + weeks Activity: A Gaggle of Girls The Ferrells have 3 children: Jennifer, Jessica, and Jaclyn. If we assume that a couple is equally
More informationChapter 4 Probability Distributions
Slide 1 Chapter 4 Probability Distributions Slide 2 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions 4-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 4-5
More informationMath : Spring 2008
Math 1070-2: Spring 2008 Lecture 7 Davar Khoshnevisan Department of Mathematics University of Utah http://www.math.utah.edu/ davar February 27, 2008 An example A WHO study of health: In Canada, the systolic
More informationHomework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a
Homework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a Announcements: There are some office hour changes for Nov 5, 8, 9 on website Week 5 quiz begins after class today and ends at
More informationProbability 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
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 informationMidTerm 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,
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 informationAMS7: WEEK 4. CLASS 3
AMS7: WEEK 4. CLASS 3 Sampling distributions and estimators. Central Limit Theorem Normal Approximation to the Binomial Distribution Friday April 24th, 2015 Sampling distributions and estimators REMEMBER:
More informationChapter 9: Sampling Distributions
Chapter 9: Sampling Distributions 9. Introduction This chapter connects the material in Chapters 4 through 8 (numerical descriptive statistics, sampling, and probability distributions, in particular) with
More informationEngineering 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
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 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 information4 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
More informationCIVL 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,
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 information4.3 Normal distribution
43 Normal distribution Prof Tesler Math 186 Winter 216 Prof Tesler 43 Normal distribution Math 186 / Winter 216 1 / 4 Normal distribution aka Bell curve and Gaussian distribution The normal distribution
More information