Chapter 5 Discrete Probability Distributions Emu

Size: px
Start display at page:

Download "Chapter 5 Discrete Probability Distributions Emu"

Transcription

1 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 distributions emu PDF is available at our online library. With our complete resources, you could find chapter 5 discrete probability distributions emu PDF or just found any kind of Books for your readings everyday. We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with chapter 5 discrete probability distributions emu. To get started finding chapter 5 discrete probability distributions emu, you are right to find our website which has a comprehensive collection of manuals listed. Our library is the biggest of these that have literally hundreds of thousands of different products represented. You will also see that there are specific sites catered to different product types or categories, brands or niches related with chapter 5 discrete probability distributions emu. So depending on what exactly you are searching, you will be able to choose ebooks to suit your own need Need to access completely for Ebook PDF chapter 5 discrete probability distributions emu You could find and download any of books you like and save it into your disk without any problem at all. We also provide a lot of books, user manual, or guidebook that related to chapter 5 discrete probability distributions emu PDF, such as ; Chapter 5: Discrete Probability Distributions chapter 5: discrete probability distributions 158 this is a probability distribution since you have the x value and the probabilities that go with it, all of the probabilities are between zero and one, and the sum of all Chapter 5 Discrete Probability Distribution this chapter explains the concepts and applications of what is called a probability distribution. in addition, special probability distributions, the binomial distribution, is explained probability distribution. i. random variables a. random variable is a variable whose values are determined by chance. a random variable is. discrete 1 / 7

2 Chapter 5 Discrete Probability Distribution chapter 5 discrete probability distribution slide 2 learning objectives 1. understand random variables and probability distributions distinguish discrete and continuous random variables. 2.able to compute expected value and variance of discrete random variable. 3. understand: 3.1. discrete uniform distribution 3.2. binomial distribution 3.3. Chapter 5: Discrete Probability Distributions 5-8 discrete probability distributions. 25. a lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. prices for 100 rats follow the following distribution: price: $10.00 $12.50 $15.00 probability: chapter 5 discrete probability distributions 5-2 random variables 1. as defined in the text, a random variable is a variable that takes on a single numerical value, determined by chance, for each outcome of a procedure. in this exercise, the random variable Chapter 5 Some Discrete Probability Distributions 24 chapter 5. some discrete probability distributions example 5.2. suppose that the probability that a ran-domly selected car need repair in a one-year period is 0:28. we randomly select 3 cars. chapter 5 discrete probability distributions. random variables... discrete probability distributions - Texas A&m... chapter 5 discrete probability distributions discrete probability distributions. the probability distribution is defined by a... the discrete uniform probability distribution is the simplest example of a discrete probability distribution given by a formula. Chapter 5: Discrete Random Variables And Their Probability... 1 chapter 5: discrete random variables and their probability distributions 5.1 random variables 5.2 probability distribution of a discrete random variable 5.3 mean and standard deviation of a discrete random variable 5.4 the binomial probability distribution 5.5 the hypergeometricprobability distribution 5.6 the poisson probability distribution Triola Chapter 5 - California State University, Northridge chapter 5 key ideas random variables discrete and continuous, expected value probability distributions properties, mean, variance and standard deviation unusual results and the rare event rule binomial distribution properties, finding probabilities section 5-1: overview chapters 1-3 involved summarization of data sets. Chapter 6 An Introduction To Discrete Probability an introduction to discrete probability if we assume that our dice are fair, namely that each of the six possibilities for a particular dice has probability 1/6, then each of the 36 rolls w 2 / 7

3 2w has probability pr(w)= we can also consider loaded dice in which there is a different distribution of probabilities. for example... Discrete Probability Distributions - Dartmouth.edu 4 chapter 1. discrete probability distributions we notice that when we tossed the coin 10,000 times, the proportion of heads was close to the \true value".5 for obtaining a head when a coin is tossed. a math-ematical model for this experiment is called bernoulli trials (see chapter 3). the Chapter 6: Continuous Probability Distributions chapter 6: continuous probability distributions chapter 5 dealt with probability distributions arising from discrete random variables. mostly that chapter focused on the binomial experiment. there are many other experiments from discrete random variables that exist but are not covered in this book. chapter 6 deals with probability distributions... chapter 5 discrete probability distributions... be represented by a single formula. the followings are the probability distributions that will be covered in this chapter: discrete uniform distribution binomial distribution... perhaps the most commonly used discrete probability distribution is the binomial distribution. - Cba.edu.kw chapter 5 student lecture notes 5-5 discrete probability distribution example: for a survey conducted by local chamber of commerce to determine number of pc s owned by a family, write the probability distribution of the pc s owned by a family. # of pc s owned frequency relative frequency Chapter 5 Discrete Distributions - University Of Toronto chapter 5 discrete distributions in this chapter we introduce discrete random variables, those who take values in a?nite or countably in?nite support set. we discuss probability mass functions and some special ex-pectations, namely, the mean, variance and standard deviation. some of the more important the binomial probability distribution properties of a binomial experiment the experiment consists of a sequence of n identical trials. two outcomes, and, are possible on each trial. the probability of a success, denoted by p, does not change from trial to trial. the trials are. Chapter 5: Joint Probability Distributions Part 1... chapter 5: joint probability distributions part 1: sections to for both discreteand continuousrandom variables we... examples for discrete r:v: s year in college vs. number of credits taken number of cigarettes smoked per day vs. day of the week chapter 5 discrete probability distributions the observations generated by different statistical 3 / 7

4 experiments have the same general type of behavior. discrete random variables associated with these experiments can be described by essentially the same probability distribution and therefore can be represented by a single formula. Important Distributions And Densities - Dartmouth.edu chapter 5 important distributions and densities 5.1 important distributions in this chapter, we describe the discrete probability distributions and the continuous probability densities that occur most often in the analysis of experiments. we will also show how one simulates these distributions and densities on a computer. discrete uniform... Discrete Probability Distributions (chapter 5) 1 discrete probability distributions (chapter 5) discrete probability distribution s requirements for a discrete probability distribution 1. each individual probability is between 0 and 1 inclusive. Probability - Chapter 5 1 Up To Now probability - chapter 5 1 up to now... chapter 3: probability (classical, relative frequency,... probability - chapter 5 7 discrete probability distribution calculations exact number of events at least a given number of events up to a given number of events. 1 chapter 5 discrete probability distributions chapter outline random variables discrete probability distributions expected value and variance the binomial probability distribution the poisson probability distribution the hypergeometricprobability distribution random variables a is a numerical Chapter 6: Discrete Probability Distributions chapter 6: discrete probability distributions 6.1 discrete random variables 6.2 the binomial probability distribution in chapter 6, we expand on the probability concepts we learned in chapter 5, and introduce the idea of a random variable. random variables are useful because they help Chapter 5, Using Excel: Discrete Probability Distributions... chapter 5, using excel: discrete probability distributions: binomial distributions expected value: there is no single function command to get expected values so you must build the table in an excel spreadsheet. { example 1: i buy one of 200 ra e tickets for $10. the sponsors then randomly select one of the tickets. - Web.ntpu.edu.tw 5 slide 5 discrete probability distributions qthe probability distribution for a random variable describes how probabilities are distributed over the values of the random variable. qa table, formula, or graph that lists all possible values a discrete random variable can assume, together with associated probabilities, is Chapter 5: Discrete Random Variables - Ucla Statistics chapter 5: discrete random variables section 5.1 random variables (ue 2.1) note: this is a combination of section 5.1 and undergraduate econometrics (ue) 2.1. recall in our discussion 4 / 7

5 on probability we started out with some random experiment that gave rise to our set of all possible outcomes s. Chapter 5: Probability And Discrete Probability... chapter 5: probability and discrete probability distribution learn. probability binomial distribution poisson distribution some popular randomizers rolling dice spinning a wheel flipping a coin drawing cards basic concepts outcome: possible result sample space(s): all possible outcomes event(a): a subset of sample space Lecture # lecture #5 chapter 5 discrete probability distributions 5-2 random variables def: a random variable, x, represents a numerical value, determined by chance, assigned to an outcome of a probability experiment. a probability distribution is a graph, table, or formula that gives the probability for each value of the random variable. Chapter 5 discrete Probability Random Variables Random... chapter 5 discrete probability distributions 2 identify the following rvs as discrete or continuous 1. the diameter of a tree 2. the number of chapters in your... consider the discrete probability distribution: p(x) x calculate calculate example 23 a) show that x is a binomial rv. Chapter 5 Normal Probability Distributions - Blogs.spsk12.net chapter 5 normal probability distributions section 5-1 introduction to normal distributions and the standard normal distribution a. the normal distribution is the most important of the continuous probability distributions. 1. definition: a normal distribution is a for a random variable x. a. Chapter 5 Discrete Random Variables - Wordpress.com chapter 5 discrete random variables random variables and their associated probability distributions are a basic component of statistical analyses. a statistician will examine the experiment or study and determine the type of observations or data it produces (con-tinuous, discrete, or categorical) and then select a random variable and its Chapter 4 Discrete Probability Distributions chapter 4 discrete probability distributions... compares a theoretical probability model to an observed one. chapter 4 9. bios 2041 statistical methods abdus s. wahed... table 4.5: probability mass function x= the number of episodes of otitis media in the?rst two years of life. Chapter 6 Discrete Probability Distributions Ch chapter 6.2 the binomial probability distribution objective a : criteria for a binomial probability experiment the binomial probability distribution is a discrete probability distribution that obtained from a binomial experiment. example 1: determine which of the following probability experiments represents a binomial experiment. Chapter 6: Random Variables And The Normal Distribution 6... chapter 6: random variables and the normal... by the end of this section, i will be able to 1) 5 / 7

6 identify random variables. 2) explain what a discrete probability distribution is and construct probability distribution tables and graphs. 3) calculate the mean, variance, and standard... probability of rolling a 5 for a fair die is 1/6,... Chapter 6: Random Variables And The Normal Distribution 6... chapter 6: random variables and the normal distribution... explain what a discrete probability distribution is and construct probability distribution tables and graphs. 3) calculate the mean, variance,... probability of rolling a 5 for a fair die is 1/6, thus p(x = 5) = 1/6. Chapter 5: Joint Probability Distributions - Webassign.net chapter 5: joint probability distributions. outline jointly distributed random variables. outline expected values, covariance and correlation.... discrete example the joint probability mass function p(x,y) gives the probability x=x and y=y for each x,y pair. for example Chapter 4 Discrete Probability Distributions 4 Discrete... chapter 4 discrete probability distributions 93 this gives the probability distribution of m as it shows how the total probability of 1 is distributed over the possible values. the probability distribution is often denoted by pm(). so p ()1 =pm()=1= 1 3, p()2 = 1 2, p()3 = 1 6. in general, px()=x=px(), and p can often be written as a formula. Chapter 5: Discrete Probability Distributions chapter 5: discrete probability distributions diana pell section 5.1: probability distributions a random variable is a variable whose values are determined by chance. a discrete probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. the probabilities are determined... - Ncue.edu.tw chapter 5 discrete probability distributions learning objectives 1. understand the concepts of a random variable and a probability distribution. 2. be able to distinguish between discrete and continuous random variables. 3. be able to compute and interpret the expected value, variance, and standard deviation for a discrete random variable. 4. Chapter 4 General Discrete Probability Distributions chapter 4 : discrete probability distributions probability distributions can be represented by tables or by formulas. in discrete probability distributions the variable can be only specified selected numerical values (such as {10, 14, 18, 21}, or {-5, -2.5, 0, 1.5, 6} or {0, 1, 2,..., n} or {all positive whole numbers}. Discrete Mathematics & Mathematical Reasoning Chapter 7... kousha etessami (u. of edinburgh, uk) discrete mathematics (chapter 7) 5 / 16 simple examples of probability distributions example 1: suppose a fair coin is tossed 7 times consecutively. Chapter 4 Discrete Probability Distributions discrete probability distributions chapter 4.1 probability distributions larson & farber, elementary statistics: picturing the world, 3e 3 random variables a random variable xrepresents 6 / 7

7 a numerical value associated with each outcome of a probability distribution. a random variable is discrete if it has a finite or countable number [chapter 5. Multivariate Probability Distributions] [chapter 5. multivariate probability distributions] 5.1 introduction 5.2 bivariate and multivariate probability dis-tributions 5.3 marginal and conditional probability dis-tributions 5.4 independent random variables 5.5 the expected value of a function of ran-dom variables 5.6 special theorems 5.7 the covariance of two random variables Sta2023. Chapter 5, Discrete Probability Distributions... chapter 5, discrete probability distributions. binomial distribution. practice 5. broward college determine whether the following is a probability distribution. if not, identify the requirement that is not satisfied. 1) if a person is randomly selected from a certain town, the probability distribution for the 7 / 7

ECON 214 Elements of Statistics for Economists 2016/2017

ECON 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 information

Chapter 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. 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 information

Discrete Random Variables and Probability Distributions

Discrete Random Variables and Probability Distributions Chapter 4 Discrete Random Variables and Probability Distributions 4.1 Random Variables A quantity resulting from an experiment that, by chance, can assume different values. A random variable is a variable

More information

Chapter 5 Student Lecture Notes 5-1. Department of Quantitative Methods & Information Systems. Business Statistics

Chapter 5 Student Lecture Notes 5-1. Department of Quantitative Methods & Information Systems. Business Statistics Chapter 5 Student Lecture Notes 5-1 Department of Quantitative Methods & Information Systems Business Statistics Chapter 5 Discrete Probability Distributions QMIS 120 Dr. Mohammad Zainal Chapter Goals

More information

Probability Distributions

Probability Distributions 4.1 Probability Distributions Random Variables A random variable x represents a numerical value associated with each outcome of a probability distribution. A random variable is discrete if it has a finite

More information

Chapter 4 Discrete Random variables

Chapter 4 Discrete Random variables Chapter 4 Discrete Random variables A is a variable that assumes numerical values associated with the random outcomes of an experiment, where only one numerical value is assigned to each sample point.

More information

Lecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series

Lecture 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 information

Chapter 4 Discrete Random variables

Chapter 4 Discrete Random variables Chapter 4 Discrete Random variables A is a variable that assumes numerical values associated with the random outcomes of an experiment, where only one numerical value is assigned to each sample point.

More information

5.2 Random Variables, Probability Histograms and Probability Distributions

5.2 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 information

Chapter 3 - Lecture 5 The Binomial Probability Distribution

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

More information

Business Statistics. Chapter 5 Discrete Probability Distributions QMIS 120. Dr. Mohammad Zainal

Business Statistics. Chapter 5 Discrete Probability Distributions QMIS 120. Dr. Mohammad Zainal Department of Quantitative Methods & Information Systems Business Statistics Chapter 5 Discrete Probability Distributions QMIS 120 Dr. Mohammad Zainal Chapter Goals After completing this chapter, you should

More information

Experimental Probability - probability measured by performing an experiment for a number of n trials and recording the number of outcomes

Experimental 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 information

Statistics for Managers Using Microsoft Excel 7 th Edition

Statistics 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 information

Discrete Random Variables

Discrete Random Variables Discrete Random Variables MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018 Objectives During this lesson we will learn to: distinguish between discrete and continuous

More information

Discrete Random Variables

Discrete Random Variables Discrete Random Variables MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2017 Objectives During this lesson we will learn to: distinguish between discrete and continuous

More information

Example 1: Identify the following random variables as discrete or continuous: a) Weight of a package. b) Number of students in a first-grade classroom

Example 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 information

Statistical Methods in Practice STAT/MATH 3379

Statistical 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 information

VIDEO 1. A random variable is a quantity whose value depends on chance, for example, the outcome when a die is rolled.

VIDEO 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 information

2011 Pearson Education, Inc

2011 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 information

Part V - Chance Variability

Part V - Chance Variability Part V - Chance Variability Dr. Joseph Brennan Math 148, BU Dr. Joseph Brennan (Math 148, BU) Part V - Chance Variability 1 / 78 Law of Averages In Chapter 13 we discussed the Kerrich coin-tossing experiment.

More information

Examples: Random Variables. Discrete and Continuous Random Variables. Probability Distributions

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:

More information

List of Online Quizzes: Quiz7: Basic Probability Quiz 8: Expectation and sigma. Quiz 9: Binomial Introduction Quiz 10: Binomial Probability

List of Online Quizzes: Quiz7: Basic Probability Quiz 8: Expectation and sigma. Quiz 9: Binomial Introduction Quiz 10: Binomial Probability List of Online Homework: Homework 6: Random Variables and Discrete Variables Homework7: Expected Value and Standard Dev of a Variable Homework8: The Binomial Distribution List of Online Quizzes: Quiz7:

More information

Statistics 6 th Edition

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

More information

Lecture 9. Probability Distributions. Outline. Outline

Lecture 9. Probability Distributions. Outline. Outline Outline Lecture 9 Probability Distributions 6-1 Introduction 6- Probability Distributions 6-3 Mean, Variance, and Expectation 6-4 The Binomial Distribution Outline 7- Properties of the Normal Distribution

More information

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 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

More information

Lecture 9. Probability Distributions

Lecture 9. Probability Distributions Lecture 9 Probability Distributions Outline 6-1 Introduction 6-2 Probability Distributions 6-3 Mean, Variance, and Expectation 6-4 The Binomial Distribution Outline 7-2 Properties of the Normal Distribution

More information

CHAPTER 10: Introducing Probability

CHAPTER 10: Introducing Probability CHAPTER 10: Introducing Probability The Basic Practice of Statistics 6 th Edition Moore / Notz / Fligner Lecture PowerPoint Slides Chapter 10 Concepts 2 The Idea of Probability Probability Models Probability

More information

Random Variables and Applications OPRE 6301

Random Variables and Applications OPRE 6301 Random Variables and Applications OPRE 6301 Random Variables... As noted earlier, variability is omnipresent in the business world. To model variability probabilistically, we need the concept of a random

More information

What do you think "Binomial" involves?

What 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 information

Lean Six Sigma: Training/Certification Books and Resources

Lean 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 information

CHAPTER 8 PROBABILITY DISTRIBUTIONS AND STATISTICS

CHAPTER 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 information

Probability Distributions for Discrete RV

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

More information

CHAPTER 4 DISCRETE PROBABILITY DISTRIBUTIONS

CHAPTER 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 information

Theory Of Stochastic Processes Cox Miller

Theory Of Stochastic Processes Cox Miller We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with theory of stochastic

More information

Probability mass function; cumulative distribution function

Probability mass function; cumulative distribution function PHP 2510 Random variables; some discrete distributions Random variables - what are they? Probability mass function; cumulative distribution function Some discrete random variable models: Bernoulli Binomial

More information

A useful modeling tricks.

A useful modeling tricks. .7 Joint models for more than two outcomes We saw that we could write joint models for a pair of variables by specifying the joint probabilities over all pairs of outcomes. In principal, we could do this

More information

The normal distribution is a theoretical model derived mathematically and not empirically.

The normal distribution is a theoretical model derived mathematically and not empirically. Sociology 541 The Normal Distribution Probability and An Introduction to Inferential Statistics Normal Approximation The normal distribution is a theoretical model derived mathematically and not empirically.

More information

2. Modeling Uncertainty

2. Modeling Uncertainty 2. Modeling Uncertainty Models for Uncertainty (Random Variables): Big Picture We now move from viewing the data to thinking about models that describe the data. Since the real world is uncertain, our

More information

Business Statistics 41000: Probability 3

Business Statistics 41000: Probability 3 Business Statistics 41000: Probability 3 Drew D. Creal University of Chicago, Booth School of Business February 7 and 8, 2014 1 Class information Drew D. Creal Email: dcreal@chicagobooth.edu Office: 404

More information

TOPIC: PROBABILITY DISTRIBUTIONS

TOPIC: 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 information

A probability distribution shows the possible outcomes of an experiment and the probability of each of these outcomes.

A probability distribution shows the possible outcomes of an experiment and the probability of each of these outcomes. Introduction In the previous chapter we discussed the basic concepts of probability and described how the rules of addition and multiplication were used to compute probabilities. In this chapter we expand

More information

Chapter 8 Additional Probability Topics

Chapter 8 Additional Probability Topics 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

More information

Random Variables Handout. Xavier Vilà

Random Variables Handout. Xavier Vilà Random Variables Handout Xavier Vilà Course 2004-2005 1 Discrete Random Variables. 1.1 Introduction 1.1.1 Definition of Random Variable A random variable X is a function that maps each possible outcome

More information

Business Statistics 41000: Probability 4

Business 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 information

Chapter 13 Financial Statement Analysis Notes

Chapter 13 Financial Statement Analysis Notes CHAPTER 13 FINANCIAL STATEMENT ANALYSIS NOTES PDF - Are you looking for chapter 13 financial statement analysis notes Books? Now, you will be happy that at this time chapter 13 financial statement analysis

More information

The Binomial Probability Distribution

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

More information

Theoretical Foundations

Theoretical Foundations Theoretical Foundations Probabilities Monia Ranalli monia.ranalli@uniroma2.it Ranalli M. Theoretical Foundations - Probabilities 1 / 27 Objectives understand the probability basics quantify random phenomena

More information

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.

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

More information

Chapter 18 International Capital Budgeting Suggested

Chapter 18 International Capital Budgeting Suggested We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with chapter 18 international

More information

Chapter 9. Idea of Probability. Randomness and Probability. Basic Practice of Statistics - 3rd Edition. Chapter 9 1. Introducing Probability

Chapter 9. Idea of Probability. Randomness and Probability. Basic Practice of Statistics - 3rd Edition. Chapter 9 1. Introducing Probability Chapter 9 Introducing Probability BPS - 3rd Ed. Chapter 9 1 Idea of Probability Probability is the science of chance behavior Chance behavior is unpredictable in the short run but has a regular and predictable

More information

STAT Chapter 7: Central Limit Theorem

STAT Chapter 7: Central Limit Theorem STAT 251 - Chapter 7: Central Limit Theorem In this chapter we will introduce the most important theorem in statistics; the central limit theorem. What have we seen so far? First, we saw that for an i.i.d

More information

Discrete Probability Distributions

Discrete 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 information

STA 220H1F LEC0201. Week 7: More Probability: Discrete Random Variables

STA 220H1F LEC0201. Week 7: More Probability: Discrete Random Variables STA 220H1F LEC0201 Week 7: More Probability: Discrete Random Variables Recall: A sample space for a random experiment is the set of all possible outcomes of the experiment. Random Variables A random variable

More information

Chapter 5. Sampling Distributions

Chapter 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 information

MA : Introductory Probability

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:

More information

Math 160 Professor Busken Chapter 5 Worksheets

Math 160 Professor Busken Chapter 5 Worksheets Math 160 Professor Busken Chapter 5 Worksheets Name: 1. Find the expected value. Suppose you play a Pick 4 Lotto where you pay 50 to select a sequence of four digits, such as 2118. If you select the same

More information

Binomial and multinomial distribution

Binomial 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 information

Econ 6900: Statistical Problems. Instructor: Yogesh Uppal

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

More information

Stat 20: Intro to Probability and Statistics

Stat 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 information

Chapter 3 The Accounting Information System

Chapter 3 The Accounting Information System CHAPTER 3 THE ACCOUNTING INFORMATION SYSTEM PDF - Are you looking for chapter 3 the accounting information system Books? Now, you will be happy that at this time chapter 3 the accounting information system

More information

Math 227 Practice Test 2 Sec Name

Math 227 Practice Test 2 Sec Name Math 227 Practice Test 2 Sec 4.4-6.2 Name Find the indicated probability. ) A bin contains 64 light bulbs of which 0 are defective. If 5 light bulbs are randomly selected from the bin with replacement,

More information

UQ, STAT2201, 2017, Lectures 3 and 4 Unit 3 Probability Distributions.

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.

More information

Probability. An intro for calculus students P= Figure 1: A normal integral

Probability. An intro for calculus students P= Figure 1: A normal integral Probability An intro for calculus students.8.6.4.2 P=.87 2 3 4 Figure : A normal integral Suppose we flip a coin 2 times; what is the probability that we get more than 2 heads? Suppose we roll a six-sided

More information

CS 237: Probability in Computing

CS 237: Probability in Computing CS 237: Probability in Computing Wayne Snyder Computer Science Department Boston University Lecture 12: Continuous Distributions Uniform Distribution Normal Distribution (motivation) Discrete vs Continuous

More information

ME3620. Theory of Engineering Experimentation. Spring Chapter III. Random Variables and Probability Distributions.

ME3620. Theory of Engineering Experimentation. Spring Chapter III. Random Variables and Probability Distributions. ME3620 Theory of Engineering Experimentation Chapter III. Random Variables and Probability Distributions Chapter III 1 3.2 Random Variables In an experiment, a measurement is usually denoted by a variable

More information

4.2 Bernoulli Trials and Binomial Distributions

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

More information

Federal Taxation Comprehensive Volume Solution Chapter 4

Federal Taxation Comprehensive Volume Solution Chapter 4 Federal Taxation Comprehensive Volume Solution Chapter 4 We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer,

More information

Math489/889 Stochastic Processes and Advanced Mathematical Finance Homework 5

Math489/889 Stochastic Processes and Advanced Mathematical Finance Homework 5 Math489/889 Stochastic Processes and Advanced Mathematical Finance Homework 5 Steve Dunbar Due Fri, October 9, 7. Calculate the m.g.f. of the random variable with uniform distribution on [, ] and then

More information

Math 243 Section 4.3 The Binomial Distribution

Math 243 Section 4.3 The Binomial Distribution Math 243 Section 4.3 The Binomial Distribution Overview Notation for the mean, standard deviation and variance The Binomial Model Bernoulli Trials Notation for the mean, standard deviation and variance

More information

Section Random Variables

Section 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 information

Chapter 3 Discrete Random Variables and Probability Distributions

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

More information

Binomial Random Variables. Binomial Random Variables

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

More information

ECON 214 Elements of Statistics for Economists 2016/2017

ECON 214 Elements of Statistics for Economists 2016/2017 ECON 214 Elements of Statistics for Economists 2016/2017 Topic The Normal Distribution Lecturer: Dr. Bernardin Senadza, Dept. of Economics bsenadza@ug.edu.gh College of Education School of Continuing and

More information

x is a random variable which is a numerical description of the outcome of an experiment.

x 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 information

Section M Discrete Probability Distribution

Section M Discrete Probability Distribution Section M Discrete Probability Distribution A random variable is a numerical measure of the outcome of a probability experiment, so its value is determined by chance. Random variables are typically denoted

More information

4 Random Variables and Distributions

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

More information

Chapter 7: Random Variables and Discrete Probability Distributions

Chapter 7: Random Variables and Discrete Probability Distributions Chapter 7: Random Variables and Discrete Probability Distributions 7. Random Variables and Probability Distributions This section introduced the concept of a random variable, which assigns a numerical

More information

Discrete Probability Distributions

Discrete Probability Distributions Discrete Probability Distributions Chapter 6 Learning Objectives Define terms random variable and probability distribution. Distinguish between discrete and continuous probability distributions. Calculate

More information

Project Economics And Decision Analysis Solution

Project Economics And Decision Analysis Solution PROJECT ECONOMICS AND DECISION ANALYSIS SOLUTION PDF - Are you looking for project economics and decision analysis solution Books? Now, you will be happy that at this time project economics and decision

More information

MA 1125 Lecture 14 - Expected Values. Wednesday, October 4, Objectives: Introduce expected values.

MA 1125 Lecture 14 - Expected Values. Wednesday, October 4, Objectives: Introduce expected values. MA 5 Lecture 4 - Expected Values Wednesday, October 4, 27 Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the

More information

Module 4: Probability

Module 4: Probability Module 4: Probability 1 / 22 Probability concepts in statistical inference Probability is a way of quantifying uncertainty associated with random events and is the basis for statistical inference. Inference

More information

Chapter 7. Sampling Distributions and the Central Limit Theorem

Chapter 7. Sampling Distributions and the Central Limit Theorem Chapter 7. Sampling Distributions and the Central Limit Theorem 1 Introduction 2 Sampling Distributions related to the normal distribution 3 The central limit theorem 4 The normal approximation to binomial

More information

Math 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 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 information

Learning Objec0ves. Statistics for Business and Economics. Discrete Probability Distribu0ons

Learning 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 information

STA 6166 Fall 2007 Web-based Course. Notes 10: Probability Models

STA 6166 Fall 2007 Web-based Course. Notes 10: Probability Models STA 6166 Fall 2007 Web-based Course 1 Notes 10: Probability Models We first saw the normal model as a useful model for the distribution of some quantitative variables. We ve also seen that if we make a

More information

Annuities. Need to access completely for Ebook PDF annuities

Annuities. Need to access completely for Ebook PDF annuities ANNUITIES PDF - Are you looking for annuities Books? Now, you will be happy that at this time annuities PDF is available at our online library. With our complete resources, you could find annuities PDF

More information

Chapter 3 Class Notes Intro to Probability

Chapter 3 Class Notes Intro to Probability Chapter 3 Class Notes Intro to Probability Concept: role a fair die, then: what is the probability of getting a 3? Getting a 3 in one roll of a fair die is called an Event and denoted E. In general, Number

More information

II - Probability. Counting Techniques. three rules of counting. 1multiplication rules. 2permutations. 3combinations

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

More information

Math 14 Lecture Notes Ch. 4.3

Math 14 Lecture Notes Ch. 4.3 4.3 The Binomial Distribution Example 1: The former Sacramento King's DeMarcus Cousins makes 77% of his free throws. If he shoots 3 times, what is the probability that he will make exactly 0, 1, 2, or

More information

Elementary Statistics Lecture 5

Elementary Statistics Lecture 5 Elementary Statistics Lecture 5 Sampling Distributions Chong Ma Department of Statistics University of South Carolina Chong Ma (Statistics, USC) STAT 201 Elementary Statistics 1 / 24 Outline 1 Introduction

More information

Random Variable: Definition

Random Variable: Definition Random Variables Random Variable: Definition A Random Variable is a numerical description of the outcome of an experiment Experiment Roll a die 10 times Inspect a shipment of 100 parts Open a gas station

More information

Basic Data Analysis. Stephen Turnbull Business Administration and Public Policy Lecture 4: May 2, Abstract

Basic Data Analysis. Stephen Turnbull Business Administration and Public Policy Lecture 4: May 2, Abstract Basic Data Analysis Stephen Turnbull Business Administration and Public Policy Lecture 4: May 2, 2013 Abstract Introduct the normal distribution. Introduce basic notions of uncertainty, probability, events,

More information

Chapter 4. Section 4.1 Objectives. Random Variables. Random Variables. Chapter 4: Probability Distributions

Chapter 4. Section 4.1 Objectives. Random Variables. Random Variables. Chapter 4: Probability Distributions Chapter 4: Probability s 4. Probability s 4. Binomial s Section 4. Objectives Distinguish between discrete random variables and continuous random variables Construct a discrete probability distribution

More information

Chapter 7. Sampling Distributions and the Central Limit Theorem

Chapter 7. Sampling Distributions and the Central Limit Theorem Chapter 7. Sampling Distributions and the Central Limit Theorem 1 Introduction 2 Sampling Distributions related to the normal distribution 3 The central limit theorem 4 The normal approximation to binomial

More information

Part 1 In which we meet the law of averages. The Law of Averages. The Expected Value & The Standard Error. Where Are We Going?

Part 1 In which we meet the law of averages. The Law of Averages. The Expected Value & The Standard Error. Where Are We Going? 1 The Law of Averages The Expected Value & The Standard Error Where Are We Going? Sums of random numbers The law of averages Box models for generating random numbers Sums of draws: the Expected Value Standard

More information

Accounting To Trial Balance 10th Edition

Accounting To Trial Balance 10th Edition ACCOUNTING TO TRIAL BALANCE 10TH EDITION PDF - Are you looking for accounting to trial balance 10th edition Books? Now, you will be happy that at this time accounting to trial balance 10th edition PDF

More information

ECO220Y Introduction to Probability Readings: Chapter 6 (skip section 6.9) and Chapter 9 (section )

ECO220Y Introduction to Probability Readings: Chapter 6 (skip section 6.9) and Chapter 9 (section ) ECO220Y Introduction to Probability Readings: Chapter 6 (skip section 6.9) and Chapter 9 (section 9.1-9.3) Fall 2011 Lecture 6 Part 2 (Fall 2011) Introduction to Probability Lecture 6 Part 2 1 / 44 From

More information

Simple Random Sample

Simple Random Sample Simple Random Sample A simple random sample (SRS) of size n consists of n elements from the population chosen in such a way that every set of n elements has an equal chance to be the sample actually selected.

More information

Chapter 5. Discrete Probability Distributions. Random Variables

Chapter 5. Discrete Probability Distributions. Random Variables Chapter 5 Discrete Probability Distributions Random Variables x is a random variable which is a numerical description of the outcome of an experiment. Discrete: If the possible values change by steps or

More information

Chapter 4 Probability Distributions

Chapter 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 information