Discrete Probability Distributions
|
|
|
- Lauren Hicks
- 5 years ago
- Views:
Transcription
1 Discrete Probability Distributions Chapter 6 McGraw-Hill/Irwin Copyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
2 Learning Objectives LO1 Identify the characteristics of a probability distribution. LO2 Distinguish between discrete and continuous random variable. LO3 Compute the mean of a probability distribution. LO4 Compute the variance and standard deviation of a probability distribution. LO5 Describe and compute probabilities for a binomial distribution. LO6 Describe and compute probabilities for a hypergeometric distribution. (Excluded) LO7 Describe and compute probabilities for a Poisson distribution. 6-2
3 LO1 Identify the characteristics of a probability distribution. What is a Probability Distribution? PROBABILITY DISTRIBUTION A listing of all the outcomes of an experiment and the probability associated with each outcome. Experiment: Toss a coin three times. Observe the number of heads. The possible results are: Zero heads, One head, Two heads, and Three heads. What is the probability distribution for the number of heads? 6-3
4 LO1 Characteristics of a Probability Distribution CHARACTERISTICS OF A PROBABILITY DISTRIBUTION 1.The probability of a particular outcome is between 0 and 1 inclusive. 2. The outcomes are mutually exclusive events. 3. The list is exhaustive. So the sum of the probabilities of the various events is equal to
5 LO1 Probability Distribution of Number of Heads Observed in 3 Tosses of a Coin 6-5
6 LO1 Random Variables RANDOM VARIABLE A quantity resulting from an experiment that, by chance, can assume different values. 6-6
7 LO2 Distinguish between discrete and continuous random variable. Types of Random Variables DISCRETE RANDOM VARIABLE A random variable that can assume only certain clearly separated values. It is usually the result of counting something. CONTINUOUS RANDOM VARIABLE can assume an infinite number of values within a given range. It is usually the result of some type of measurement 6-7
8 LO2 Discrete Random Variables DISCRETE RANDOM VARIABLE A random variable that can assume only certain clearly separated values. It is usually the result of counting something. EXAMPLES 1. The number of students in a class. 2. The number of children in a family. 3. The number of cars entering a carwash in a hour. 4. Number of home mortgages approved by Coastal Federal Bank last week. 6-8
9 LO2 Continuous Random Variables CONTINUOUS RANDOM VARIABLE can assume an infinite number of values within a given range. It is usually the result of some type of measurement EXAMPLES The length of each song on the latest Tim McGraw album. The weight of each student in this class. The temperature outside as you are reading this book. The amount of money earned by each of the more than 750 players currently on Major League Baseball team rosters. 6-9
10 LO3 Compute the mean of a probability distribution. The Mean of a Probability Distribution MEAN The mean is a typical value used to represent the central location of a probability distribution. The mean of a probability distribution is also referred to as its expected value. 6-10
11 LO3 Mean, Variance, and Standard Deviation of a Probability Distribution - Example John Ragsdale sells new cars for Pelican Ford. John usually sells the largest number of cars on Saturday. He has developed the following probability distribution for the number of cars he expects to sell on a particular Saturday. 6-11
12 LO3 Mean of a Probability Distribution - Example 6-12
13 LO4 Compute the variance and standard deviation of a probability distribution. The Variance and Standard Deviation of a Probability Distribution Measures the amount of spread in a distribution The computational steps are: 1. Subtract the mean from each value, and square this difference. 2. Multiply each squared difference by its probability. 3. Sum the resulting products to arrive at the variance. The standard deviation is found by taking the positive square root of the variance. 6-13
14 LO4 Variance and Standard Deviation of a Probability Distribution - Example 2 σ = σ = =
Discrete Probability Distributions
Discrete Probability Distributions Chapter 6 McGraw-Hill/Irwin Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved. GOALS 6-2 1. Define the terms probability distribution and random variable.
Discrete Probability Distributions
Discrete Probability Distributions Chapter 6 Copyright 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Learning
Probability Distributions. Chapter 6
Probability Distributions Chapter 6 McGraw-Hill/Irwin The McGraw-Hill Companies, Inc. 2008 Types of Random Variables Discrete Random Variable can assume only certain clearly separated values. It is usually
Probability Distributions. Chapter 6
Probability Distributions Chapter 6 McGraw-Hill/Irwin The McGraw-Hill Companies, Inc. 2008 GOALS Define the terms probability distribution and random variable. Distinguish between discrete and continuous
GOALS. Discrete Probability Distributions. A Distribution. What is a Probability Distribution? Probability for Dice Toss. A Probability Distribution
GOALS Discrete Probability Distributions Chapter 6 Dr. Richard Jerz Define the terms probability distribution and random variable. Distinguish between discrete and continuous probability distributions.
Discrete Probability Distributions Chapter 6 Dr. Richard Jerz
Discrete Probability Distributions Chapter 6 Dr. Richard Jerz 1 GOALS Define the terms probability distribution and random variable. Distinguish between discrete and continuous 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
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
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
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
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
AP Statistics Chapter 6 - Random Variables
AP Statistics Chapter 6 - Random 6.1 Discrete and Continuous Random Objective: Recognize and define discrete random variables, and construct a probability distribution table and a probability histogram
CHAPTER 6 Random Variables
CHAPTER 6 Random Variables 6.1 Discrete and Continuous Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Discrete and Continuous Random
Measuring Risk. Expected value and expected return 9/4/2018. Possibilities, Probabilities and Expected Value
Chapter Five Understanding Risk Introduction Risk cannot be avoided. Everyday decisions involve financial and economic risk. How much car insurance should I buy? Should I refinance my mortgage now or later?
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
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:
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
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
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
Random Variables and Probability Functions
University of Central Arkansas Random Variables and Probability Functions Directory Table of Contents. Begin Article. Stephen R. Addison Copyright c 001 saddison@mailaps.org Last Revision Date: February
Basics of Probability
Basics of Probability By A.V. Vedpuriswar October 2, 2016 2, 2016 Random variables and events A random variable is an uncertain quantity. A outcome is an observed value of a random variable. An event is
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
Probability Models.S2 Discrete Random Variables
Probability Models.S2 Discrete Random Variables Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard Results of an experiment involving uncertainty are described by one or more random
Discrete Probability Distributions
6 Learning Objectives When you have completed this chapter, you will be able to: Discrete Probability Distributions LO1 Identify the characteristics of a probability distribution. LO2 Distinguish between
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
A 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
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
Chapter 7: Random Variables
Chapter 7: Random Variables 7.1 Discrete and Continuous Random Variables 7.2 Means and Variances of Random Variables 1 Introduction A random variable is a function that associates a unique numerical value
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
Shifting our focus. We were studying statistics (data, displays, sampling...) The next few lectures focus on probability (randomness) Why?
Probability Introduction Shifting our focus We were studying statistics (data, displays, sampling...) The next few lectures focus on probability (randomness) Why? What is Probability? Probability is used
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.
Estimation and Confidence Intervals
Estimation and Confidence Intervals Chapter 9-1/2 McGraw-Hill/Irwin Copyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved. LEARNING OBJECTIVES LO1. Define a point estimate. LO2. Define
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
Chapter 5. Discrete Probability Distributions. McGraw-Hill, Bluman, 7 th ed, Chapter 5 1
Chapter 5 Discrete Probability Distributions McGraw-Hill, Bluman, 7 th ed, Chapter 5 1 Chapter 5 Overview Introduction 5-1 Probability Distributions 5-2 Mean, Variance, Standard Deviation, and Expectation
MAKING SENSE OF DATA Essentials series
MAKING SENSE OF DATA Essentials series THE NORMAL DISTRIBUTION Copyright by City of Bradford MDC Prerequisites Descriptive statistics Charts and graphs The normal distribution Surveys and sampling Correlation
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
1 A Brief History of. Chapter. Risk and Return. Dollar Returns. PercentReturn. Learning Objectives. A Brief History of Risk and Return
Chapter Learning Objectives To become a wise investor (maybe even one with too much money), you need to know: 1 A Brief History of Risk and Return How to calculate the return on an investment using different
Chapter 17. The. Value Example. The Standard Error. Example The Short Cut. Classifying and Counting. Chapter 17. The.
Context Short Part V Chance Variability and Short Last time, we learned that it can be helpful to take real-life chance processes and turn them into a box model. outcome of the chance process then corresponds
Chapter 6: Random Variables
Chapter 6: Random Variables Section 6.1 Discrete and Continuous Random Variables The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 6 Random Variables 6.1 Discrete and Continuous
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.
Estimation and Confidence Intervals
Estimation and Confidence Intervals Chapter 9-2/2 McGraw-Hill/Irwin Copyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved. A Confidence Interval for a Proportion (π) Learning Objective
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.
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
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
Department of Quantitative Methods & Information Systems. Business Statistics. Chapter 6 Normal Probability Distribution QMIS 120. Dr.
Department of Quantitative Methods & Information Systems Business Statistics Chapter 6 Normal Probability Distribution QMIS 120 Dr. Mohammad Zainal Chapter Goals After completing this chapter, you should
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
Chapter 3. Discrete Probability Distributions
Chapter 3 Discrete Probability Distributions 1 Chapter 3 Overview Introduction 3-1 The Binomial Distribution 3-2 Other Types of Distributions 2 Chapter 3 Objectives Find the exact probability for X successes
Mathematics of Randomness
Ch 5 Probability: The Mathematics of Randomness 5.1.1 Random Variables and Their Distributions A random variable is a quantity that (prior to observation) can be thought of as dependent on chance phenomena.
Random Variables Part 2
Random Variables Part 2 1 A P S T A T I S T I C S C H A P T E R 1 5 The theory of probabilities is simply the science of logic quantitatively treated. Charles Saunders Peirce (1839-1914) Behavior of Random
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
Sec$on 6.1: Discrete and Con.nuous Random Variables. Tuesday, November 14 th, 2017
Sec$on 6.1: Discrete and Con.nuous Random Variables Tuesday, November 14 th, 2017 Discrete and Continuous Random Variables Learning Objectives After this section, you should be able to: ü COMPUTE probabilities
Continuous Probability Distributions
Continuous Probability Distributions Chapter 7 McGraw-Hill/Irwin Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved. GOALS 1. Understand the difference between discrete and continuous
12/1/2017. Chapter. Copyright 2009 by The McGraw-Hill Companies, Inc. 8B-2
Sampling Distributions and Estimation (Part ) 8 Chapter Proportion C.I. for the Difference of Two s, m 1 -m C.I. for the Difference of Two Proportions, p 1 -p Population Variance, s McGraw-Hill/Irwin Copyright
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.
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
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
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
Chapter 5 Discrete Probability Distributions. Random Variables Discrete Probability Distributions Expected Value and Variance
Chapter 5 Discrete Probability Distributions Random Variables Discrete Probability Distributions Expected Value and Variance.40.30.20.10 0 1 2 3 4 Random Variables A random variable is a numerical description
Chapter 7. Random Variables
Chapter 7 Random Variables Making quantifiable meaning out of categorical data Toss three coins. What does the sample space consist of? HHH, HHT, HTH, HTT, TTT, TTH, THT, THH In statistics, we are most
Bayes s Rule Example. defective. An MP3 player is selected at random and found to be defective. What is the probability it came from Factory I?
Bayes s Rule Example A company manufactures MP3 players at two factories. Factory I produces 60% of the MP3 players and Factory II produces 40%. Two percent of the MP3 players produced at Factory I are
Example - Let X be the number of boys in a 4 child family. Find the probability distribution table:
Chapter7 Probability Distributions and Statistics Distributions of Random Variables tthe value of the result of the probability experiment is a RANDOM VARIABLE. Example - Let X be the number of boys in
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
Some 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
MATH 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
A 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
Lecture 7 Random Variables
Lecture 7 Random Variables Definition: A random variable is a variable whose value is a numerical outcome of a random phenomenon, so its values are determined by chance. We shall use letters such as X
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
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
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
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
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
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
Central Limit Theorem 11/08/2005
Central Limit Theorem 11/08/2005 A More General Central Limit Theorem Theorem. Let X 1, X 2,..., X n,... be a sequence of independent discrete random variables, and let S n = X 1 + X 2 + + X n. For each
Chapter 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
Chapter 3 Discrete Random Variables and Probability Distributions
Chapter 3 Discrete Random Variables and Probability Distributions Part 2: Mean and Variance of a Discrete Random Variable Section 3.4 1 / 16 Discrete Random Variable - Expected Value In a random experiment,
Model Paper Statistics Objective. Paper Code Time Allowed: 20 minutes
Model Paper Statistics Objective Intermediate Part I (11 th Class) Examination Session 2012-2013 and onward Total marks: 17 Paper Code Time Allowed: 20 minutes Note:- You have four choices for each objective
Population Mean GOALS. Characteristics of the Mean. EXAMPLE Population Mean. Parameter Versus Statistics. Describing Data: Numerical Measures
GOALS Describing Data: Numerical Measures Chapter 3 McGraw-Hill/Irwin Copyright 010 by The McGraw-Hill Companies, Inc. All rights reserved. 3-1. Calculate the arithmetic mean, weighted mean, median, mode,
Binomial Random Variables
Models for Counts Solutions COR1-GB.1305 Statistics and Data Analysis Binomial Random Variables 1. A certain coin has a 25% of landing heads, and a 75% chance of landing tails. (a) If you flip the coin
Chapter 5 Basic Probability
Chapter 5 Basic Probability Probability is determining the probability that a particular event will occur. Probability of occurrence = / T where = the number of ways in which a particular event occurs
CHAPTER 7 RANDOM VARIABLES AND DISCRETE PROBABILTY DISTRIBUTIONS MULTIPLE CHOICE QUESTIONS
CHAPTER 7 RANDOM VARIABLES AND DISCRETE PROBABILTY DISTRIBUTIONS MULTIPLE CHOICE QUESTIONS In the following multiple-choice questions, please circle the correct answer.. The weighted average of the possible
We use probability distributions to represent the distribution of a discrete random variable.
Now we focus on discrete random variables. We will look at these in general, including calculating the mean and standard deviation. Then we will look more in depth at binomial random variables which are
5.06 Rationalizing Denominators
.0 Rationalizing Denominators There is a tradition in mathematics of eliminating the radicals from the denominators (or numerators) of fractions. The process is called rationalizing the denominator (or
EXCEL STATISTICAL Functions. Presented by Wayne Wilmeth
EXCEL STATISTICAL Functions Presented by Wayne Wilmeth Exponents 2 3 Exponents 2 3 2*2*2 = 8 Exponents Exponents Exponents Exponent Examples Roots? *? = 81? *? *? = 27 Roots =Sqrt(81) 9 Roots 27 1/3 27^(1/3)
The 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
+ Chapter 7. Random Variables. Chapter 7: Random Variables 2/26/2015. Transforming and Combining Random Variables
+ Chapter 7: Random Variables Section 7.1 Discrete and Continuous Random Variables The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE + Chapter 7 Random Variables 7.1 7.2 7.2 Discrete
Mean of a Discrete Random variable. Suppose that X is a discrete random variable whose distribution is : :
Dr. Kim s Note (December 17 th ) The values taken on by the random variable X are random, but the values follow the pattern given in the random variable table. What is a typical value of a random variable
5.3 Standard Deviation
Math 2201 Date: 5.3 Standard Deviation Standard Deviation We looked at range as a measure of dispersion, or spread of a data set. The problem with using range is that it is only a measure of how spread
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
Data Analytics (CS40003) Practice Set IV (Topic: Probability and Sampling Distribution)
Data Analytics (CS40003) Practice Set IV (Topic: Probability and Sampling Distribution) I. Concept Questions 1. Give an example of a random variable in the context of Drawing a card from a deck of cards.
Random Variables. 6.1 Discrete and Continuous Random Variables. Probability Distribution. Discrete Random Variables. Chapter 6, Section 1
6.1 Discrete and Continuous Random Variables Random Variables A random variable, usually written as X, is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types
STOR 155 Introductory Statistics (Chap 5) Lecture 14: Sampling Distributions for Counts and Proportions
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics (Chap 5) Lecture 14: Sampling Distributions for Counts and Proportions 5/31/11 Lecture 14 1 Statistic & Its Sampling Distribution
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
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
ASSIGNMENT 14 section 10 in the probability and statistics module
McMaster University Math 1LT3 ASSIGNMENT 14 section 10 in the probability and statistics module 1. (a) A shipment of 2,000 containers has arrived at the port of Vancouver. As part of the customs inspection,
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
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
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
Discrete probability distributions
Discrete probability distributions Probability distributions Discrete random variables Expected values (mean) Variance Linear functions - mean & standard deviation Standard deviation 1 Probability distributions
Sampling & populations
Sampling & populations Sample proportions Sampling distribution - small populations Sampling distribution - large populations Sampling distribution - normal distribution approximation Mean & variance of
A random variable X is a function that assigns (real) numbers to the elements of the sample space S of a random experiment.
RANDOM VARIABLES and PROBABILITY DISTRIBUTIONS A random variable X is a function that assigns (real) numbers to the elements of the samle sace S of a random exeriment. The value sace V of a random variable