SECTION 4.4: Expected Value
|
|
- Helen Holmes
- 5 years ago
- Views:
Transcription
1 15 SECTION 4.4: Expected Value This section tells you why most all gambling is a bad idea. And also why carnival or amusement park games are a bad idea. Random Variables Definition: Random Variable A random variable is a rule that assigns precisely one real number to each outcome of an experiment. Example 1: Random Variable for Grades Texas A&M University (and most all other universities) use letters to denote grades. Each letter grade also has a specific number attached to it, namely Example 2: Defining a Random Variable for Flipping Coins A fair coin is flipped three times. We are interested in keeping track of the number of heads in each trial. a) Associate a random variable with the outcomes to keep track of the number of heads, b) Give the probability distribution table for the random variable.
2 16 Histograms are a graphical way to represent how probability is distributed. To create a histogram: List the options for your random variable along the The represents probability For each random variable outcome x, over x draw a rectangle with a base of 1 unit and the height being equal to the probability P(X = x) of that random variable number Example 3: Histogram for Flipping Coins In Example 2, we let X be the random variable that assigned the to each outcome the number of times heads appeared. The probability distribution table was as follows: x (# heads) P(X=x) 1/8 3/8 3/8 1/8 The corresponding histogram would be:
3 17 Example 4: Baseball Histogram Suppose that the number of singles, doubles, triples, homeruns, and no-hits were recorded for a certain baseball player for 465 times-at-bat. Let the random variable R be 0 for no-hits, 1 for a single, 2 for a double, 3 for a triple, and 4 for a homerun. a) Find the probability distribution for any given at-bat being a 0, 1, 2, 3, or 4, given the data below. Event No Hit Single Double Triple Homerun Frequency R P(X = x) b) Create the histogram for the random variable R c) Use the histogram to find the probability that the player gets on base for any random at-bat
4 18 Expected Value Expected value is a special kind of average that tells us what to expect for an experiment over the long term. Definition: Expected Value Let X denote the random variable that has values x!, x!, x!,, x!, and let the associated probabilities be p!, p!, p!,, p!. (That is to say,,, and so on). Then the (or mean) of the random variable X, denote by, is given by: E X = x! p! + x! p! + x! p! + + x! p! Example 5: Calculating Expected Value Suppose X is a random variable whose values and probabilities are given by the following table: Random variable, x P(X = x) a) Find the expected value, E(X). b) Find the expected value on your calculator.
5 19 Example 8: Expected Value A fair 6-sided die is tossed. Let X be the random variable assigning the number rolled to each outcome. Find E(X). Example 6: Expected Value of Coins One coin is taken at random from a bag containing 3 nickels, 4 dimes, and 7 quarters. Let X be the value of the coin selected. Find E(X). Example 7: Finding Random Variable & Expected Value of Game A game costs $3 to play. A fair 6-sided die is rolled. If you roll an even number, you win the amount of money equal to the number rolled. Otherwise, you win nothing. Find the expected net winnings for this game.
6 20 Example 8: Finding Insurance Premium A man wants to purchase a life insurance policy that will pay the beneficiary $30,000 in the event that the man s death occurs during the next year. The probability that the man will live another year is What is the minimum amount the man will pay for his premium? (Hint: the minimum premium amount occurs when the life insurance company s expected profit is zero) Example 10: Probability Distribution The probability distribution for a random variable X is given above. Find the following: a) P(X = 0) b) P(X 0) c) P( 1 < X 4) d) P(X 1)
Chapter 3: Probability Distributions and Statistics
Chapter 3: Probability Distributions and Statistics Section 3.-3.3 3. Random Variables and Histograms A is a rule that assigns precisely one real number to each outcome of an experiment. We usually denote
More informationLearning Goals: * Determining the expected value from a probability distribution. * Applying the expected value formula to solve problems.
Learning Goals: * Determining the expected value from a probability distribution. * Applying the expected value formula to solve problems. The following are marks from assignments and tests in a math class.
More informationProbability Distribution Unit Review
Probability Distribution Unit Review Topics: Pascal's Triangle and Binomial Theorem Probability Distributions and Histograms Expected Values, Fair Games of chance Binomial Distributions Hypergeometric
More 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 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 informationVIDEO 1. A random variable is a quantity whose value depends on chance, for example, the outcome when a die is rolled.
Part 1: Probability Distributions VIDEO 1 Name: 11-10 Probability and Binomial Distributions A random variable is a quantity whose value depends on chance, for example, the outcome when a die is rolled.
More informationSection 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 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 information111, section 8.2 Expected Value
111, section 8.2 Expected Value notes prepared by Tim Pilachowski Do you remember how to calculate an average? The word average, however, has connotations outside of a strict mathematical definition, so
More informationWhat do you think "Binomial" involves?
Learning Goals: * Define a binomial experiment (Bernoulli Trials). * Applying the binomial formula to solve problems. * Determine the expected value of a Binomial Distribution What do you think "Binomial"
More informationPart 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 informationSection Distributions of Random Variables
Section 8.1 - Distributions of Random Variables Definition: A random variable is a rule that assigns a number to each outcome of an experiment. Example 1: Suppose we toss a coin three times. Then we could
More informationDiscrete 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 informationDiscrete 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 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 informationSTOR 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
More informationHave you ever wondered whether it would be worth it to buy a lottery ticket every week, or pondered on questions such as If I were offered a choice
Section 8.5: Expected Value and Variance Have you ever wondered whether it would be worth it to buy a lottery ticket every week, or pondered on questions such as If I were offered a choice between a million
More informationMATH1215: Mathematical Thinking Sec. 08 Spring Worksheet 9: Solution. x P(x)
N. Name: MATH: Mathematical Thinking Sec. 08 Spring 0 Worksheet 9: Solution Problem Compute the expected value of this probability distribution: x 3 8 0 3 P(x) 0. 0.0 0.3 0. Clearly, a value is missing
More information***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 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 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 informationSection Distributions of Random Variables
Section 8.1 - Distributions of Random Variables Definition: A random variable is a rule that assigns a number to each outcome of an experiment. Example 1: Suppose we toss a coin three times. Then we could
More informationMA 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 informationvariance risk Alice & Bob are gambling (again). X = Alice s gain per flip: E[X] = Time passes... Alice (yawning) says let s raise the stakes
Alice & Bob are gambling (again). X = Alice s gain per flip: risk E[X] = 0... Time passes... Alice (yawning) says let s raise the stakes E[Y] = 0, as before. Are you (Bob) equally happy to play the new
More informationProbability 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 informationProbability and Statistics. Copyright Cengage Learning. All rights reserved.
Probability and Statistics Copyright Cengage Learning. All rights reserved. 14.3 Binomial Probability Copyright Cengage Learning. All rights reserved. Objectives Binomial Probability The Binomial Distribution
More informationProbability 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 informationTRINITY COLLGE DUBLIN
TRINITY COLLGE DUBLIN School of Computer Science and Statistics Extra Questions ST3009: Statistical Methods for Computer Science NOTE: There are many more example questions in Chapter 4 of the course textbook
More informationCentral 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
More informationStatistical Methods in Practice STAT/MATH 3379
Statistical Methods in Practice STAT/MATH 3379 Dr. A. B. W. Manage Associate Professor of Mathematics & Statistics Department of Mathematics & Statistics Sam Houston State University Overview 6.1 Discrete
More informationMath 166: Topics in Contemporary Mathematics II
Math 166: Topics in Contemporary Mathematics II Ruomeng Lan Texas A&M University October 15, 2014 Ruomeng Lan (TAMU) Math 166 October 15, 2014 1 / 12 Mean, Median and Mode Definition: 1. The average or
More informationChapter 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 informationExample. Chapter 8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables
Chapter 8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables You are dealt a hand of 5 cards. Find the probability distribution table for the number of hearts. Graph
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Module 5 Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Calculate the specified probability ) Suppose that T is a random variable. Given
More informationThe 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 informationSection 8.1 Distributions of Random Variables
Section 8.1 Distributions of Random Variables Random Variable A random variable is a rule that assigns a number to each outcome of a chance experiment. There are three types of random variables: 1. Finite
More informationMath 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 information1. Steve says I have two children, one of which is a boy. Given this information, what is the probability that Steve has two boys?
Chapters 6 8 Review 1. Steve says I have two children, one of which is a boy. Given this information, what is the probability that Steve has two boys? (A) 1 (B) 3 1 (C) 3 (D) 4 1 (E) None of the above..
More information6.1 Binomial Theorem
Unit 6 Probability AFM Valentine 6.1 Binomial Theorem Objective: I will be able to read and evaluate binomial coefficients. I will be able to expand binomials using binomial theorem. Vocabulary Binomial
More 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 informationConsider the following examples: ex: let X = tossing a coin three times and counting the number of heads
Overview Both chapters and 6 deal with a similar concept probability distributions. The difference is that chapter concerns itself with discrete probability distribution while chapter 6 covers continuous
More informationChapter 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 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 informationSection 8.1 Distributions of Random Variables
Section 8.1 Distributions of Random Variables Random Variable A random variable is a rule that assigns a number to each outcome of a chance experiment. There are three types of random variables: 1. Finite
More informationMath 361. Day 8 Binomial Random Variables pages 27 and 28 Inv Do you have ESP? Inv. 1.3 Tim or Bob?
Math 361 Day 8 Binomial Random Variables pages 27 and 28 Inv. 1.2 - Do you have ESP? Inv. 1.3 Tim or Bob? Inv. 1.1: Friend or Foe Review Is a particular study result consistent with the null model? Learning
More informationStatistics, Their Distributions, and the Central Limit Theorem
Statistics, Their Distributions, and the Central Limit Theorem MATH 3342 Sections 5.3 and 5.4 Sample Means Suppose you sample from a popula0on 10 0mes. You record the following sample means: 10.1 9.5 9.6
More informationSection Random Variables and Histograms
Section 3.1 - Random Variables and Histograms Definition: A random variable is a rule that assigns a number to each outcome of an experiment. Example 1: Suppose we toss a coin three times. Then we could
More informationChapter 11. Data Descriptions and Probability Distributions. Section 4 Bernoulli Trials and Binomial Distribution
Chapter 11 Data Descriptions and Probability Distributions Section 4 Bernoulli Trials and Binomial Distribution 1 Learning Objectives for Section 11.4 Bernoulli Trials and Binomial Distributions The student
More informationDiscrete Random Variables
Discrete Random Variables In this chapter, we introduce a new concept that of a random variable or RV. A random variable is a model to help us describe the state of the world around us. Roughly, a RV can
More informationEx 1) Suppose a license plate can have any three letters followed by any four digits.
AFM Notes, Unit 1 Probability Name 1-1 FPC and Permutations Date Period ------------------------------------------------------------------------------------------------------- The Fundamental Principle
More informationSTA 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 informationSection 3.1 Distributions of Random Variables
Section 3.1 Distributions of Random Variables Random Variable A random variable is a rule that assigns a number to each outcome of a chance experiment. There are three types of random variables: 1. Finite
More information5.4 Normal Approximation of the Binomial Distribution
5.4 Normal Approximation of the Binomial Distribution Bernoulli Trials have 3 properties: 1. Only two outcomes - PASS or FAIL 2. n identical trials Review from yesterday. 3. Trials are independent - probability
More 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 informationChapter Chapter 6. Modeling Random Events: The Normal and Binomial Models
Chapter 6 107 Chapter 6 Modeling Random Events: The Normal and Binomial Models Chapter 6 108 Chapter 6 109 Table Number: Group Name: Group Members: Discrete Probability Distribution: Ichiro s Hit Parade
More informationStatistics, Measures of Central Tendency I
Statistics, Measures of Central Tendency I We are considering a random variable X with a probability distribution which has some parameters. We want to get an idea what these parameters are. We perfom
More informationRandom variables. Discrete random variables. Continuous random variables.
Random variables Discrete random variables. Continuous random variables. Discrete random variables. Denote a discrete random variable with X: It is a variable that takes values with some probability. Examples:
More informationProblem Set 07 Discrete Random Variables
Name Problem Set 07 Discrete Random Variables MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean of the random variable. 1) The random
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 informationExample - Let X be the number of boys in a 4 child family. Find the probability distribution table:
Chapter8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables tthe value of the result of the probability experiment is a RANDOM VARIABLE. Example - Let X be the number
More informationEcon 6900: Statistical Problems. Instructor: Yogesh Uppal
Econ 6900: Statistical Problems Instructor: Yogesh Uppal Email: yuppal@ysu.edu Lecture Slides 4 Random Variables Probability Distributions Discrete Distributions Discrete Uniform Probability Distribution
More informationOCR Statistics 1. Discrete random variables. Section 2: The binomial and geometric distributions. When to use the binomial distribution
Discrete random variables Section 2: The binomial and geometric distributions Notes and Examples These notes contain subsections on: When to use the binomial distribution Binomial coefficients Worked examples
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 informationx is a random variable which is a numerical description of the outcome of an experiment.
Chapter 5 Discrete Probability Distributions Random Variables is a random variable which is a numerical description of the outcome of an eperiment. Discrete: If the possible values change by steps or jumps.
More informationProblem A Grade x P(x) To get "C" 1 or 2 must be 1 0.05469 B A 2 0.16410 3 0.27340 4 0.27340 5 0.16410 6 0.05470 7 0.00780 0.2188 0.5468 0.2266 Problem B Grade x P(x) To get "C" 1 or 2 must 1 0.31150 be
More informationAssignment 3 - Statistics. n n! (n r)!r! n = 1,2,3,...
Assignment 3 - Statistics Name: Permutation: Combination: n n! P r = (n r)! n n! C r = (n r)!r! n = 1,2,3,... n = 1,2,3,... The Fundamental Counting Principle: If two indepndent events A and B can happen
More information5. In fact, any function of a random variable is also a random variable
Random Variables - Class 11 October 14, 2012 Debdeep Pati 1 Random variables 1.1 Expectation of a function of a random variable 1. Expectation of a function of a random variable 2. We know E(X) = x xp(x)
More informationA 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 informationChapter 14. From Randomness to Probability. Copyright 2010 Pearson Education, Inc.
Chapter 14 From Randomness to Probability Copyright 2010 Pearson Education, Inc. Dealing with Random Phenomena A random phenomenon is a situation in which we know what outcomes could happen, but we don
More information5.7 Probability Distributions and Variance
160 CHAPTER 5. PROBABILITY 5.7 Probability Distributions and Variance 5.7.1 Distributions of random variables We have given meaning to the phrase expected value. For example, if we flip a coin 100 times,
More informationX P(X=x) E(X)= V(X)= S.D(X)= X P(X=x) E(X)= V(X)= S.D(X)=
1. X 0 1 2 P(X=x) 0.2 0.4 0.4 E(X)= V(X)= S.D(X)= X 100 200 300 400 P(X=x) 0.1 0.2 0.5 0.2 E(X)= V(X)= S.D(X)= 2. A day trader buys an option on a stock that will return a $100 profit if the stock goes
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 informationMath 14 Lecture Notes Ch The Normal Approximation to the Binomial Distribution. P (X ) = nc X p X q n X =
6.4 The Normal Approximation to the Binomial Distribution Recall from section 6.4 that g A binomial experiment is a experiment that satisfies the following four requirements: 1. Each trial can have only
More informationMATH 112 Section 7.3: Understanding Chance
MATH 112 Section 7.3: Understanding Chance Prof. Jonathan Duncan Walla Walla University Autumn Quarter, 2007 Outline 1 Introduction to Probability 2 Theoretical vs. Experimental Probability 3 Advanced
More informationShifting 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
More informationbinomial day 1.notebook December 10, 2013 Probability Quick Review of Probability Distributions!
Probability Binomial Distributions Day 1 Quick Review of Probability Distributions! # boys born in 4 births, x 0 1 2 3 4 Probability, P(x) 0.0625 0.25 0.375 0.25 0.0625 TWO REQUIREMENTS FOR A PROBABILITY
More 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 informationX = x p(x) 1 / 6 1 / 6 1 / 6 1 / 6 1 / 6 1 / 6. x = 1 x = 2 x = 3 x = 4 x = 5 x = 6 values for the random variable X
Calculus II MAT 146 Integration Applications: Probability Calculating probabilities for discrete cases typically involves comparing the number of ways a chosen event can occur to the number of ways all
More informationSimple 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 informationLet X be the number that comes up on the next roll of the die.
Chapter 6 - Discrete Probability Distributions 6.1 Random Variables Introduction If we roll a fair die, the possible outcomes are the numbers 1, 2, 3, 4, 5, and 6, and each of these numbers has probability
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 informationStatistics 511 Additional Materials
Discrete Random Variables In this section, we introduce the concept of a random variable or RV. A random variable is a model to help us describe the state of the world around us. Roughly, a RV can be thought
More informationStatistics for Managers Using Microsoft Excel 7 th Edition
Statistics for Managers Using Microsoft Excel 7 th Edition Chapter 5 Discrete Probability Distributions Statistics for Managers Using Microsoft Excel 7e Copyright 014 Pearson Education, Inc. Chap 5-1 Learning
More informationBinomial 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
More informationChapter 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 informationExample - 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
More informationMath 1070 Sample Exam 2 Spring 2015
University of Connecticut Department of Mathematics Math 1070 Sample Exam 2 Spring 2015 Name: Instructor Name: Section: Exam 2 will cover Sections 4.6-4.7, 5.3-5.4, 6.1-6.4, and F.1-F.4. This sample exam
More informationBusiness 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 informationChapter 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 informationTOPIC: PROBABILITY DISTRIBUTIONS
TOPIC: PROBABILITY DISTRIBUTIONS There are two types of random variables: A Discrete random variable can take on only specified, distinct values. A Continuous random variable can take on any value within
More informationThe 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
More information4.1 Probability Distributions
Probability and Statistics Mrs. Leahy Chapter 4: Discrete Probability Distribution ALWAYS KEEP IN MIND: The Probability of an event is ALWAYS between: and!!!! 4.1 Probability Distributions Random Variables
More informationTheoretical 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 informationExperimental Probability - probability measured by performing an experiment for a number of n trials and recording the number of outcomes
MDM 4U Probability Review Properties of Probability Experimental Probability - probability measured by performing an experiment for a number of n trials and recording the number of outcomes Theoretical
More informationProf. Thistleton MAT 505 Introduction to Probability Lecture 3
Sections from Text and MIT Video Lecture: Sections 2.1 through 2.5 http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systemsanalysis-and-applied-probability-fall-2010/video-lectures/lecture-1-probability-models-and-axioms/
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 informationMean 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
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 informationFINAL REVIEW W/ANSWERS
FINAL REVIEW W/ANSWERS ( 03/15/08 - Sharon Coates) Concepts to review before answering the questions: A population consists of the entire group of people or objects of interest to an investigator, while
More informationStatistics for Business and Economics: Random Variables (1)
Statistics for Business and Economics: Random Variables (1) STT 315: Section 201 Instructor: Abdhi Sarkar Acknowledgement: I d like to thank Dr. Ashoke Sinha for allowing me to use and edit the slides.
More information