You may use your calculator and a single page of notes. The room is crowded. Please be careful to look only at your own exam.
|
|
- Tracy Lee
- 5 years ago
- Views:
Transcription
1 LAST NAME (Please Print): KEY FIRST NAME (Please Print): HONOR PLEDGE (Please Sign): Statistics 111 Midterm 1 This is a closed book exam. You may use your calculator and a single page of notes. The room is crowded. Please be careful to look only at your own exam. Report all numerical answers to at least two correct decimal places or (when appropriate) write them as a fraction. All question parts count for 1 point, unless otherwise indicated. 1
2 1. A retirement home has two television rooms. At 9 p.m. on Sunday, residents must choose which of two new shows to watch: Game of Cards or House of Thrones. Out of 50 people who watched Game of Cards, 40 liked it. Among the 50 who watched House of Thrones, only 20 liked it. The following Sunday, one of the television sets breaks down. The director decides that everyone should watch Game of Cards, since it was more popular. But Nurse Ratchet knows that of the audience for Game of Cards consisted of 45 Democrats and 5 Republicans, and that all 5 Republicans hated the show. And of the audience for House of Thrones, there were 10 Democrats and 40 Republicans, and 8 Democrats liked the show. The first step is to put the information into a table, such as the following. In the parentheses, I ve listed Democrats first, then Republicans: Like Not Like Game of Cards (40, 0) (5, 5) House of Thrones (8, 12) (2, 28) 0 What percentage of Republicans like Game of Cards? From the table, 0%. 30% What percentage of Republicans like House of Thrones? 12/(12+28), or 30% or 0.58 What is Nurse Ratchet s estimate of the proportion of people who will like House of Thrones? In terms of the Berkeley example, like/dislike is accept/reject, GoC/HoT is male/female, and R/D is like major. So the formula is proportion of Dems * prop. of Dems who like HoT + proportion of Reps * proportion of Reps who like HoT = (55/100) (8/10) + (45/100)(12/40) = How does Nurse Ratchet explain the situation to the director? Democrats tend to like television shows, but Republicans don t. More Democrats saw GoC, so it seemed more popular, but that was misleading. 2
3 2. A high school has 20 each of freshmen, sophomores and juniors, and 10 seniors. The proportions of women in each group are 50%, 50%, 60% and 70%, respectively. Fresh Soph Jr Sr Male Female What is the probability that a random person is a woman or a freshman? From the table, 49/70 = You draw three people at random. What is the probability that all three are males? ( 31 3 ) ( 39 0 ) ( 70 / 3 ) = In 1930, the Health and Nutrition Examination took a random sample of adults and recorded their weight. In 2005, the CDC looked at the lifespans of those participants and found that people who weighed less lived longer. Based on this, the CDC decided that obesity was a critical health issue. Yes Was this an observational study? What confounding variable might explain these findings? Why? Age. People tend to gain weight as they grow older. So people with low weights tend to be young, and have more time on their clocks. 4. Suppose that 30% of the patrons in a bar are women. You measure everyone s height. 3
4 F True or False: You expect the median to be less than the average. The mean is pulled down by the smaller heights of the women, but the median is resistant to outliers. T True or False: You expect the sd to be larger than you would find in a bar whose clientele was exclusively male. Because there is more spread in the data when it is a mixture of shorter women and taller men. 5. Consider the following numbers: 6.5 (a) What is the IQR? 1, 8, 9, 10, 7, 8, 4, 2 As in class, the 25th percentile is any number between 1 and 2, thus 1.5, and the 75th percentile is between 8 and 8, or 8. And = What is the standard deviation? Routine calculation. Note that there is no reason to think that this is a sample from a larger population. 30 Suppose a set of numbers has standard deviation equal to 6. If you multiply each number by -5 and subtract 10, then what is the new range? The new sd is the absolute value of the multiplier times the old, or 5 * 6. 0 Suppose a set of numbers has median equal to -2. If you multiply each number by -5 and subtract 10, then what is the new median? The new median is the same operation applied to the old, or (-5)*(-2) - 10 = 0. 4
5 0.68 to A decorticator is a device for shelling nuts (usually by shooting the nut at a surface with a precise amount of force and orientation). To test your new decorticator, you fire 100 nuts. Suppose the decorticator correctly extracts the meat 90% of the time. What is the approximate probability that more than 88 nuts are properly shelled? Use the normal approximation to the binomial with a continuity correction. The mean of the binomial is np = 90 and the standard deviation is np(1 p) = 3. Thus the probability that X > 88 is approximately the probability that z > ( )/3. 7. The joint density of (X,Y ) is f(x,y) = 6(x y) for 0 < y < x < 1. What is the marginal density of y? Integrate the joint density with respect to x; note that the limits of integration for x are from y up to 1. You get f Y (y) = 3(1 2y + y 2 ) on 0 y 1. What is the conditional density of x given y? Since f X Y = f(x,y)/f Y (y), then the conditional density is f X Y (x y) = 2(x y)/(1 2y + y 2 ). 5/6 What is the expected value of X when y = 0.5? IE[X Y = 0.5] = x2(x 0.5)/(1 2(0.5) + (0.5)2 )dx = 5/6. 1/80 What is the covariance between X and Y? (Assume that IE[X] = 3/4.) We need IE[XY ] and IE[Y ]. IE[XY ] = 1 x 0 0 xy 6(x y)dydx = 1/5 5
6 and IE[Y ] = 1 0 y 3(1 2y + y 2 )dy = 1/4 so the covariance is IE[XY ] IE[X] IE[Y ] = (1/5) (1/4)(3/4) = 1/80. 1/3 What is the correlation between X and Y? (Assume that Var [X] = 3/80.) The correlation is the covariance divided by the product of the standard deviations of X and Y. The standard deviation of X is given as 3/80. To find the variance of Y we first need IE[Y 2 ] = 1 0 y2 3(1 2y y 2 )dy = 1/10. Then Var [Y ] = 1/10 (1/4) 2 = 3/80. So the standard deviation of Y is 3/80. Thus the correlation is 1/3. Note: You could have immediately deduced that the variances of X and Y are equal, by the symmetry in the joint density function. 8. There are three brands of medical pacemakers. Heart Throb controls 40% of the market, The Body Electric controls 25%, and the rest is owned by The Beat Goes On. The failure rate for Heart Throb devices is 1%. The failure rate for The Body Electric is 2%. And the failure rate for The Beat Goes On is 4%. If the chief engineer at the FDA s Center for Devices and Radiological Health dies from a pacemaker failure, what is the probability that he carried a Heart Throb? Bayes rule. (0.01)*(0.4)/[(0.01)*(0.4) + (0.02)*(0.25) + (0.04)*(0.35)] = Los Alamos controls 20 missiles, of which 8 are inoperable. In order to renew their contract from the Department of Energy, they have to successfully demonstrate two launches. They randomly choose a missile to launch, try it, and continue until they have had two successful launches. What is the probability that they terminate on the third try? (Comment: This is called inverse sampling, and is useful when each try is risky or expensive.) In order to get the second success on the third trial, there must have been one success and one failure on the first two trials, followed by a success. The probability of a success and failure on the first two is hypergeometric with 12 successes, 8 failures, 2 ). Given that outcome, the probability ( ) ( ) ( draws, and 1 success, or / that the next launch is a success is 11/18. The product of these is
7 Shakespeare wrote 10 historical plays. An English professor wants to pick three to assign to his class for reading. In how many ways could he select them? (Assume that the order does not matter.) ( 10 3 ) In how many ways can 6 people sit at a circular table? (That is, one s neighbors matter but not which chair one selects and not whether your neighbor sits to the left or right.) Imagine that the chairs are numbered. Then there are 6! ways for the people to sit in order. But since this is a circle, 6 of those are equivalent. And since left/right doesn t matter, 2 more arrangements are equivalent. Thus there are 6!/(6*2) = 60 ways to do this On average, people have 2.8 car accidents. What is the chance that a random person will have three or more accidents in their life? Poisson /0!e /1!e /2!e 2.8 = Suppose that 20% of students love statistics. What is the chance that three or more people among ten whom you meet at The Perk enjoy their statistics course? ( 10 Binomial. 1 0 ) ( ) ( ) = A Poisson process describes the timing of random events, such as celebrity deaths. The time between events is exponential with rate λ, and the number of events in a unit time period has the Poisson distribution with parameter λ. 1 exp( λ) What is the probability that time between two successive events is less than one day? 7
8 1 exp ( λ) What is the formula for the probability that the count is 1 or more in one day? Explain. In a Poisson process, if the waiting time is greater than one unit, then no events occur in that time period. Thus the probability that the time is less than one unit has to equal the probability at one or more events occur. 8
You may use your calculator and a single page of notes. The room is crowded. Please be careful to look only at your own exam.
LAST NAME (Please Print): FIRST NAME (Please Print): HONOR PLEDGE (Please Sign): Statistics 111 Midterm 1 This is a closed book exam. You may use your calculator and a single page of notes. The room is
More informationTest 3 SOLUTIONS. x P(x) xp(x)
16 1. A couple of weeks ago in class, each of you took three quizzes where you randomly guessed the answers to each question. There were eight questions on each quiz, and four possible answers to each
More informationYou may use your calculator and a single page of notes.
LAST NAME (Please Print): KEY FIRST NAME (Please Print): HONOR PLEDGE (Please Sign): Statistics 111 Midterm 2 This is a closed book exam. You may use your calculator and a single page of notes. The room
More information1. Let X be a random variable with probability density function. 1 x < f(x) = 0 otherwise
Name M36K Final. Let X be a random variable with probability density function { /x x < f(x = 0 otherwise Compute the following. You can leave your answers in integral form. (a ( points Find F X (t = P
More informationStat 2300 International, Fall 2006 Sample Midterm. Friday, October 20, Your Name: A Number:
Stat 2300 International, Fall 2006 Sample Midterm Friday, October 20, 2006 Your Name: A Number: The Midterm consists of 35 questions: 20 multiple-choice questions (with exactly 1 correct answer) and 15
More informationMATH 1150 Chapter 2 Notation and Terminology
MATH 1150 Chapter 2 Notation and Terminology Categorical Data The following is a dataset for 30 randomly selected adults in the U.S., showing the values of two categorical variables: whether or not the
More information4. Suppose that we roll two die and let X be equal to the maximum of the two rolls. Find P (X {1, 3, 5}) and draw the PMF for X.
Math 10B with Professor Stankova Worksheet, Midterm #2; Wednesday, 3/21/2018 GSI name: Roy Zhao 1 Problems 1.1 Bayes Theorem 1. Suppose a test is 99% accurate and 1% of people have a disease. What is the
More informationMath 1040 Sample Final Examination. Problem Points Score Total 200
Name: Math 1040 Sample Final Examination Relax and good luck! Problem Points Score 1 25 2 25 3 25 4 25 5 25 6 25 7 25 8 25 Total 200 1. (25 points) The systolic blood pressures of 20 elderly patients in
More informationChapter 3 Probability Distributions and Statistics Section 3.1 Random Variables and Histograms
Math 166 (c)2013 Epstein Chapter 3 Page 1 Chapter 3 Probability Distributions and Statistics Section 3.1 Random Variables and Histograms The value of the result of the probability experiment is called
More informationYou may use a calculator. Translation: Show all of your work; use a calculator only to do final calculations and/or to check your work.
GROUND RULES: Print your name at the top of this page. This is a closed-book and closed-notes exam. You may use a calculator. Translation: Show all of your work; use a calculator only to do final calculations
More informationMATH 227 CP 7 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
MATH 227 CP 7 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the mean, µ, for the binomial distribution which has the stated values of n and p.
More informationIntroduction to Statistics
Chapter 1 Introduction to Statistics 1.1 Preliminary Definitions Definition 1.1. Data are observations (such as measurements, genders, survey responses) that have been collected. Definition 1.2. Statistics
More informationBusiness Statistics Midterm Exam Fall 2015 Russell. Please sign here to acknowledge
Business Statistics Midterm Exam Fall 5 Russell Name Do not turn over this page until you are told to do so. You will have hour and 3 minutes to complete the exam. There are a total of points divided into
More informationSTAT/MA 416 Answers Homework 6 November 15, 2007 Solutions by Mark Daniel Ward PROBLEMS
STAT/MA 4 Answers Homework November 5, 27 Solutions by Mark Daniel Ward PROBLEMS Chapter Problems 2a. The mass p, corresponds to neither of the first two balls being white, so p, 8 7 4/39. The mass p,
More information1 Basic continuous random variable problems
Name M362K Final Here are problems concerning material from Chapters 5 and 6. To review the other chapters, look over previous practice sheets for the two exams, previous quizzes, previous homeworks and
More information3.2 Probability Rules
3.2 Probability Rules The idea of probability rests on the fact that chance behavior is predictable in the long run. In the last section, we used simulation to imitate chance behavior. Do we always need
More informationYou may use your calculator and a single page of notes.
LAST NAME (Please Print): KEY FIRST NAME (Please Print): HONOR PLEDGE (Please Sign): Statistics 111 Midterm 4 This is a closed book exam. You may use your calculator and a single page of notes. The room
More information7.1: What is a Sampling Distribution?!?!
7.1: What is a Sampling Distribution?!?! Section 7.1 What Is a Sampling Distribution? After this section, you should be able to DISTINGUISH between a parameter and a statistic DEFINE sampling distribution
More information( ) P A B : Probability of A given B. Probability that A happens
A B A or B One or the other or both occurs At least one of A or B occurs Probability Review A B A and B Both A and B occur ( ) P A B : Probability of A given B. Probability that A happens given that B
More informationElementary Statistics
Elementary Statistics Q: What is data? Q: What does the data look like? Q: What conclusions can we draw from the data? Q: Where is the middle of the data? Q: Why is the spread of the data important? Q:
More informationTable of z values and probabilities for the standard normal distribution. z is the first column plus the top row. Each cell shows P(X z).
Table of z values and probabilities for the standard normal distribution. z is the first column plus the top row. Each cell shows P(X z). For example P(X.04) =.8508. For z < 0 subtract the value from,
More informationSalt Lake Community College MATH 1040 Final Exam Fall Semester 2011 Form E
Salt Lake Community College MATH 1040 Final Exam Fall Semester 011 Form E Name Instructor Time Limit: 10 minutes Any hand-held calculator may be used. Computers, cell phones, or other communication devices
More informationAP Final Review II Exploring Data (20% 30%)
AP Final Review II Exploring Data (20% 30%) Quantitative vs Categorical Variables Quantitative variables are numerical values for which arithmetic operations such as means make sense. It is usually a measure
More informationDiscrete Distributions
Discrete Distributions STA 281 Fall 2011 1 Introduction Previously we defined a random variable to be an experiment with numerical outcomes. Often different random variables are related in that they have
More informationProbability: Why do we care? Lecture 2: Probability and Distributions. Classical Definition. What is Probability?
Probability: Why do we care? Lecture 2: Probability and Distributions Sandy Eckel seckel@jhsph.edu 22 April 2008 Probability helps us by: Allowing us to translate scientific questions into mathematical
More informationChapter 15 Sampling Distribution Models
Chapter 15 Sampling Distribution Models 1 15.1 Sampling Distribution of a Proportion 2 Sampling About Evolution According to a Gallup poll, 43% believe in evolution. Assume this is true of all Americans.
More informationPROBABILITY.
PROBABILITY PROBABILITY(Basic Terminology) Random Experiment: If in each trial of an experiment conducted under identical conditions, the outcome is not unique, but may be any one of the possible outcomes,
More informationACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 2 MATH00040 SEMESTER / Probability
ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 2 MATH00040 SEMESTER 2 2017/2018 DR. ANTHONY BROWN 5.1. Introduction to Probability. 5. Probability You are probably familiar with the elementary
More informationand the Sample Mean Random Sample
MATH 183 Random Samples and the Sample Mean Dr. Neal, WKU Henceforth, we shall assume that we are studying a particular measurement X from a population! for which the mean µ and standard deviation! are
More informationStat 20 Midterm 1 Review
Stat 20 Midterm Review February 7, 2007 This handout is intended to be a comprehensive study guide for the first Stat 20 midterm exam. I have tried to cover all the course material in a way that targets
More informationSUMMARY OF PROBABILITY CONCEPTS SO FAR (SUPPLEMENT FOR MA416)
SUMMARY OF PROBABILITY CONCEPTS SO FAR (SUPPLEMENT FOR MA416) D. ARAPURA This is a summary of the essential material covered so far. The final will be cumulative. I ve also included some review problems
More informationProbability and Probability Distributions. Dr. Mohammed Alahmed
Probability and Probability Distributions 1 Probability and Probability Distributions Usually we want to do more with data than just describing them! We might want to test certain specific inferences about
More informationPractice problems from chapters 2 and 3
Practice problems from chapters and 3 Question-1. For each of the following variables, indicate whether it is quantitative or qualitative and specify which of the four levels of measurement (nominal, ordinal,
More informationCS 109 Midterm Review!
CS 109 Midterm Review! Major Topics: Counting and Combinatorics Probability Conditional Probability Random Variables Discrete/Continuous Distributions Joint Distributions and Convolutions Counting Sum
More informationIntroduction to Probability, Fall 2009
Introduction to Probability, Fall 2009 Math 30530 Review questions for exam 1 solutions 1. Let A, B and C be events. Some of the following statements are always true, and some are not. For those that are
More informationSection 2.3: One Quantitative Variable: Measures of Spread
Section 2.3: One Quantitative Variable: Measures of Spread Objectives: 1) Measures of spread, variability a. Range b. Standard deviation i. Formula ii. Notation for samples and population 2) The 95% rule
More informationHonors Algebra 1 - Fall Final Review
Name: Period Date: Honors Algebra 1 - Fall Final Review This review packet is due at the beginning of your final exam. In addition to this packet, you should study each of your unit reviews and your notes.
More informationUniversity of Chicago Graduate School of Business. Business 41000: Business Statistics
Name: OUTLINE SOLUTION University of Chicago Graduate School of Business Business 41000: Business Statistics Special Notes: 1. This is a closed-book exam. You may use an 8 11 piece of paper for the formulas.
More informationStats Review Chapter 6. Mary Stangler Center for Academic Success Revised 8/16
Stats Review Chapter Revised 8/1 Note: This review is composed of questions similar to those found in the chapter review and/or chapter test. This review is meant to highlight basic concepts from the course.
More informationThis does not cover everything on the final. Look at the posted practice problems for other topics.
Class 7: Review Problems for Final Exam 8.5 Spring 7 This does not cover everything on the final. Look at the posted practice problems for other topics. To save time in class: set up, but do not carry
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MGF 1106 Math for Liberal Arts I Summer 2008 - Practice Final Exam Dr. Schnackenberg If you do not agree with the given answers, answer "E" for "None of the above". MULTIPLE CHOICE. Choose the one alternative
More informationProbability Experiments, Trials, Outcomes, Sample Spaces Example 1 Example 2
Probability Probability is the study of uncertain events or outcomes. Games of chance that involve rolling dice or dealing cards are one obvious area of application. However, probability models underlie
More informationMultiple Choice Circle the letter corresponding to the best answer for each of the problems below (4 pts each)
Math 221 Hypothetical Exam 1, Wi2008, (Chapter 1-5 in Moore, 4th) April 3, 2063 S. K. Hyde, S. Barton, P. Hurst, K. Yan Name: Show all your work to receive credit. All answers must be justified to get
More information2. AXIOMATIC PROBABILITY
IA Probability Lent Term 2. AXIOMATIC PROBABILITY 2. The axioms The formulation for classical probability in which all outcomes or points in the sample space are equally likely is too restrictive to develop
More informationMath 140 Introductory Statistics
5. Models of Random Behavior Math 40 Introductory Statistics Professor Silvia Fernández Chapter 5 Based on the book Statistics in Action by A. Watkins, R. Scheaffer, and G. Cobb. Outcome: Result or answer
More informationExercises from Chapter 3, Section 1
Exercises from Chapter 3, Section 1 1. Consider the following sample consisting of 20 numbers. (a) Find the mode of the data 21 23 24 24 25 26 29 30 32 34 39 41 41 41 42 43 48 51 53 53 (b) Find the median
More informationMath 140 Introductory Statistics
Math 140 Introductory Statistics Professor Silvia Fernández Lecture 8 Based on the book Statistics in Action by A. Watkins, R. Scheaffer, and G. Cobb. 5.1 Models of Random Behavior Outcome: Result or answer
More informationMATH 407 FINAL EXAM May 6, 2011 Prof. Alexander
MATH 407 FINAL EXAM May 6, 2011 Prof. Alexander Problem Points Score 1 22 2 18 Last Name: First Name: USC ID: Signature: 3 20 4 21 5 27 6 18 7 25 8 28 Total 175 Points total 179 but 175 is maximum. This
More informationWhat is statistics? Statistics is the science of: Collecting information. Organizing and summarizing the information collected
What is statistics? Statistics is the science of: Collecting information Organizing and summarizing the information collected Analyzing the information collected in order to draw conclusions Two types
More informationHomework 9 (due November 24, 2009)
Homework 9 (due November 4, 9) Problem. The join probability density function of X and Y is given by: ( f(x, y) = c x + xy ) < x
More informationThis is a multiple choice and short answer practice exam. It does not count towards your grade. You may use the tables in your book.
NAME (Please Print): HONOR PLEDGE (Please Sign): statistics 101 Practice Final Key This is a multiple choice and short answer practice exam. It does not count towards your grade. You may use the tables
More informationORF 245 Fundamentals of Engineering Statistics. Midterm Exam 1
Princeton University Department of Operations Research and Financial Engineering ORF 45 Fundamentals of Engineering Statistics Midterm Exam March 06, 009 0:00am-0:50am PLEASE DO NOT TURN THIS PAGE AND
More informationMath 407: Probability Theory 5/10/ Final exam (11am - 1pm)
Math 407: Probability Theory 5/10/2013 - Final exam (11am - 1pm) Name: USC ID: Signature: 1. Write your name and ID number in the spaces above. 2. Show all your work and circle your final answer. Simplify
More informationChapter 7 Sampling Distributions
Statistical inference looks at how often would this method give a correct answer if it was used many many times. Statistical inference works best when we produce data by random sampling or randomized comparative
More information6.2A Linear Transformations
6.2 Transforming and Combining Random Variables 6.2A Linear Transformations El Dorado Community College considers a student to be full time if he or she is taking between 12 and 18 credits. The number
More informationSenior Math Circles November 19, 2008 Probability II
University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Senior Math Circles November 9, 2008 Probability II Probability Counting There are many situations where
More informationThis is a closed-notebook, closed laptop exam. You may use your calculator and a single page of notes.
NAME (Please Print): KEY HONOR PLEDGE (Please Sign): Statistics 80FCS Midterm 2 This is a closed-notebook, closed laptop exam. You may use your calculator and a single page of notes. The room is crowded.
More informationLet us think of the situation as having a 50 sided fair die; any one number is equally likely to appear.
Probability_Homework Answers. Let the sample space consist of the integers through. {, 2, 3,, }. Consider the following events from that Sample Space. Event A: {a number is a multiple of 5 5, 0, 5,, }
More informationTopic 3: Introduction to Statistics. Algebra 1. Collecting Data. Table of Contents. Categorical or Quantitative? What is the Study of Statistics?!
Topic 3: Introduction to Statistics Collecting Data We collect data through observation, surveys and experiments. We can collect two different types of data: Categorical Quantitative Algebra 1 Table of
More informationCounting principles, including permutations and combinations.
1 Counting principles, including permutations and combinations. The binomial theorem: expansion of a + b n, n ε N. THE PRODUCT RULE If there are m different ways of performing an operation and for each
More informationProbability and Discrete Distributions
AMS 7L LAB #3 Fall, 2007 Objectives: Probability and Discrete Distributions 1. To explore relative frequency and the Law of Large Numbers 2. To practice the basic rules of probability 3. To work with the
More informationChapters 3.2 Discrete distributions
Chapters 3.2 Discrete distributions In this section we study several discrete distributions and their properties. Here are a few, classified by their support S X. There are of course many, many more. For
More informationSTT 315 Problem Set #3
1. A student is asked to calculate the probability that x = 3.5 when x is chosen from a normal distribution with the following parameters: mean=3, sd=5. To calculate the answer, he uses this command: >
More informationStatistics 1. Edexcel Notes S1. Mathematical Model. A mathematical model is a simplification of a real world problem.
Statistics 1 Mathematical Model A mathematical model is a simplification of a real world problem. 1. A real world problem is observed. 2. A mathematical model is thought up. 3. The model is used to make
More informationMath 3 Proportion & Probability Part 2 Sequences, Patterns, Frequency Tables & Venn Diagrams
Math 3 Proportion & Probability Part 2 Sequences, Patterns, Frequency Tables & Venn Diagrams 1 MATH 2 REVIEW ARITHMETIC SEQUENCES In an Arithmetic Sequence the difference between one term and the next
More information# of 6s # of times Test the null hypthesis that the dice are fair at α =.01 significance
Practice Final Exam Statistical Methods and Models - Math 410, Fall 2011 December 4, 2011 You may use a calculator, and you may bring in one sheet (8.5 by 11 or A4) of notes. Otherwise closed book. The
More informationLecture 2: Probability and Distributions
Lecture 2: Probability and Distributions Ani Manichaikul amanicha@jhsph.edu 17 April 2007 1 / 65 Probability: Why do we care? Probability helps us by: Allowing us to translate scientific questions info
More informationProbability, For the Enthusiastic Beginner (Exercises, Version 1, September 2016) David Morin,
Chapter 8 Exercises Probability, For the Enthusiastic Beginner (Exercises, Version 1, September 2016) David Morin, morin@physics.harvard.edu 8.1 Chapter 1 Section 1.2: Permutations 1. Assigning seats *
More informationDo Now 18 Balance Point. Directions: Use the data table to answer the questions. 2. Explain whether it is reasonable to fit a line to the data.
Do Now 18 Do Now 18 Balance Point Directions: Use the data table to answer the questions. 1. Calculate the balance point.. Explain whether it is reasonable to fit a line to the data.. The data is plotted
More informationProbability 5-4 The Multiplication Rules and Conditional Probability
Outline Lecture 8 5-1 Introduction 5-2 Sample Spaces and 5-3 The Addition Rules for 5-4 The Multiplication Rules and Conditional 5-11 Introduction 5-11 Introduction as a general concept can be defined
More informationThe area under a probability density curve between any two values a and b has two interpretations:
Chapter 7 7.1 The Standard Normal Curve Introduction Probability density curve: The area under a probability density curve between any two values a and b has two interpretations: 1. 2. The region above
More informationObjective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode.
Chapter 3 Numerically Summarizing Data Chapter 3.1 Measures of Central Tendency Objective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode. A1. Mean The
More informationMath 416 Lecture 2 DEFINITION. Here are the multivariate versions: X, Y, Z iff P(X = x, Y = y, Z =z) = p(x, y, z) of X, Y, Z iff for all sets A, B, C,
Math 416 Lecture 2 DEFINITION. Here are the multivariate versions: PMF case: p(x, y, z) is the joint Probability Mass Function of X, Y, Z iff P(X = x, Y = y, Z =z) = p(x, y, z) PDF case: f(x, y, z) is
More informationMath 20 Spring Discrete Probability. Midterm Exam
Math 20 Spring 203 Discrete Probability Midterm Exam Thursday April 25, 5:00 7:00 PM Your name (please print): Instructions: This is a closed book, closed notes exam. Use of calculators is not permitted.
More informationPRACTICE PROBLEMS FOR EXAM 1
PRACTICE PROBLEMS FOR EXAM 1 Math 3160Q Spring 01 Professor Hohn Below is a list of practice questions for Exam 1. Any quiz, homework, or example problem has a chance of being on the exam. For more practice,
More informationBinomial and Poisson Probability Distributions
Binomial and Poisson Probability Distributions Esra Akdeniz March 3, 2016 Bernoulli Random Variable Any random variable whose only possible values are 0 or 1 is called a Bernoulli random variable. What
More information1 Basic continuous random variable problems
Name M362K Final Here are problems concerning material from Chapters 5 and 6. To review the other chapters, look over previous practice sheets for the two exams, previous quizzes, previous homeworks and
More informationChapter 8: Confidence Intervals
Chapter 8: Confidence Intervals Introduction Suppose you are trying to determine the mean rent of a two-bedroom apartment in your town. You might look in the classified section of the newspaper, write
More informationSection 7.2 Homework Answers
25.5 30 Sample Mean P 0.1226 sum n b. The two z-scores are z 25 20(1.7) n 1.0 20 sum n 2.012 and z 30 20(1.7) n 1.0 0.894, 20 so the probability is approximately 0.1635 (0.1645 using Table A). P14. a.
More informationQUESTION 1 50 FOR JSS 1
QUESTION 1 5 FOR JSS 1 1. The LCM of, 3 and 4 is A. 14 B. 1 C. 1 D. 16. Estimate 578.6998 to 3 decimal places. A. 578.7 B. 578.79 C. 578.8 D. 579. 3. Express 111 two as a number in base ten. A. 15 B. 18
More informationMath Fall 2010 Some Old Math 302 Exams There is always a danger when distributing old exams for a class that students will rely on them
Math 302.102 Fall 2010 Some Old Math 302 Exams There is always a danger when distributing old exams for a class that students will rely on them solely for their final exam preparations. The final exam
More informationIntroduction to Statistics
Introduction to Statistics Data and Statistics Data consists of information coming from observations, counts, measurements, or responses. Statistics is the science of collecting, organizing, analyzing,
More informationChapter 6. Exploring Data: Relationships. Solutions. Exercises:
Chapter 6 Exploring Data: Relationships Solutions Exercises: 1. (a) It is more reasonable to explore study time as an explanatory variable and the exam grade as the response variable. (b) It is more reasonable
More informationStatistics 100 Exam 2 March 8, 2017
STAT 100 EXAM 2 Spring 2017 (This page is worth 1 point. Graded on writing your name and net id clearly and circling section.) PRINT NAME (Last name) (First name) net ID CIRCLE SECTION please! L1 (MWF
More informationUCSD CSE 21, Spring 2014 [Section B00] Mathematics for Algorithm and System Analysis
UCSD CSE 21, Spring 2014 [Section B00] Mathematics for Algorithm and System Analysis Lecture 8 Class URL: http://vlsicad.ucsd.edu/courses/cse21-s14/ Lecture 8 Notes Goals for Today Counting Partitions
More informationFrancine s bone density is 1.45 standard deviations below the mean hip bone density for 25-year-old women of 956 grams/cm 2.
Chapter 3 Solutions 3.1 3.2 3.3 87% of the girls her daughter s age weigh the same or less than she does and 67% of girls her daughter s age are her height or shorter. According to the Los Angeles Times,
More informationFinal Exam Review. Name: Class: Date: Short Answer
Name: Class: Date: ID: A Final Exam Review Short Answer. Use x, 2, 0,, 2 to graph the function f( x) 2 x. Then graph its inverse. Describe the domain and range of the inverse function. 2. Graph the inverse
More informationDepartment of Statistical Science FIRST YEAR EXAM - SPRING 2017
Department of Statistical Science Duke University FIRST YEAR EXAM - SPRING 017 Monday May 8th 017, 9:00 AM 1:00 PM NOTES: PLEASE READ CAREFULLY BEFORE BEGINNING EXAM! 1. Do not write solutions on the exam;
More informationSTAT:5100 (22S:193) Statistical Inference I
STAT:5100 (22S:193) Statistical Inference I Week 3 Luke Tierney University of Iowa Fall 2015 Luke Tierney (U Iowa) STAT:5100 (22S:193) Statistical Inference I Fall 2015 1 Recap Matching problem Generalized
More informationSampling, Frequency Distributions, and Graphs (12.1)
1 Sampling, Frequency Distributions, and Graphs (1.1) Design: Plan how to obtain the data. What are typical Statistical Methods? Collect the data, which is then subjected to statistical analysis, which
More informationProblem # Number of points 1 /20 2 /20 3 /20 4 /20 5 /20 6 /20 7 /20 8 /20 Total /150
Name Student ID # Instructor: SOLUTION Sergey Kirshner STAT 516 Fall 09 Practice Midterm #1 January 31, 2010 You are not allowed to use books or notes. Non-programmable non-graphic calculators are permitted.
More informationDecember 2010 Mathematics 302 Name Page 2 of 11 pages
December 2010 Mathematics 302 Name Page 2 of 11 pages [9] 1. An urn contains red balls, 10 green balls and 1 yellow balls. You randomly select balls, without replacement. (a What ( is( the probability
More informationSTAT/SOC/CSSS 221 Statistical Concepts and Methods for the Social Sciences. Random Variables
STAT/SOC/CSSS 221 Statistical Concepts and Methods for the Social Sciences Random Variables Christopher Adolph Department of Political Science and Center for Statistics and the Social Sciences University
More informationExercise 1. Exercise 2. Lesson 2 Theoretical Foundations Probabilities Solutions You ip a coin three times.
Lesson 2 Theoretical Foundations Probabilities Solutions monia.ranalli@uniroma3.it Exercise 1 You ip a coin three times. 1. Use a tree diagram to show the possible outcome patterns. How many outcomes are
More informationMath 10 - Compilation of Sample Exam Questions + Answers
Math 10 - Compilation of Sample Exam Questions + Sample Exam Question 1 We have a population of size N. Let p be the independent probability of a person in the population developing a disease. Answer the
More informationACMS Statistics for Life Sciences. Chapter 13: Sampling Distributions
ACMS 20340 Statistics for Life Sciences Chapter 13: Sampling Distributions Sampling We use information from a sample to infer something about a population. When using random samples and randomized experiments,
More informationORF 245 Fundamentals of Engineering Statistics. Final Exam
Princeton University Department of Operations Research and Financial Engineering ORF 45 Fundamentals of Engineering Statistics Final Exam May 15, 009 1:30pm-4:30pm PLEASE DO NOT TURN THIS PAGE AND START
More information3.3. Section. Measures of Central Tendency and Dispersion from Grouped Data. Copyright 2013, 2010 and 2007 Pearson Education, Inc.
Section 3.3 Measures of Central Tendency and Dispersion from Grouped Data Objectives 1. Approximate the mean of a variable from grouped data 2. Compute the weighted mean 3. Approximate the standard deviation
More informationChapter. Numerically Summarizing Data Pearson Prentice Hall. All rights reserved
Chapter 3 Numerically Summarizing Data Section 3.1 Measures of Central Tendency Objectives 1. Determine the arithmetic mean of a variable from raw data 2. Determine the median of a variable from raw data
More informationLecture Notes for BUSINESS STATISTICS - BMGT 571. Chapters 1 through 6. Professor Ahmadi, Ph.D. Department of Management
Lecture Notes for BUSINESS STATISTICS - BMGT 571 Chapters 1 through 6 Professor Ahmadi, Ph.D. Department of Management Revised May 005 Glossary of Terms: Statistics Chapter 1 Data Data Set Elements Variable
More information