ACMS Section 02 Elements of Statistics October 28, Midterm Examination II


 Buddy Morrison
 2 years ago
 Views:
Transcription
1 ACMS Section 02 Elements of Statistics October 28, 2010 Midterm Examination II Name DO NOT remove this answer page. DO turn in the entire exam. Make sure that you have all ten (10) pages of the examination this page and 9 pages of the exam. Put your name on this sheet and put your name or initials on each page, in case pages accidentally become separated. You have 75 minutes to complete the examination. You may leave earlier if you are finished. Calculators are allowed, however, please turn off and put away all cell phones, laptops, and other electronic devices (except calculators). Remember that you are taking this examination under the University Honor Code. Record Answers to Multiple Choice Questions Here. Indicate each answer by placing an X in the appropriate circle or by filling it in. a b c d e a b c d e Please do not write in the table below. Question(s) Maximum Score Totals 100
2 Multiple Choice Section 4 points each Choose the best response to each question. Indicate your answer by placing an X in the appropriate circle on the cover page. Do NOT circle the answer. No partial credit is possible on this part of the examination. 1. In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is a women or is earning an A. a b. 0.8 c d e A oneweek study revealed that 60% of the customers of a warehouse store are women and that 30% of women customers spend at least $250 on a single visit to the store. Find the probability that a randomly chosen customer will be a woman who spends at least $250. a b c d e. None of the above 3. Which of the following best characterizes a random sample? a. All members of the sample voluntarily provide all information requested in a timely manner. b. No member of the sample is allowed to communicate with any other member of the sample. c. Methods are employed to guarantee that all subgroups of the population are represented in the sample. d. Every subset of the population with n elements, where n is the sample size, has an equal probability of being chosen. e. No individual in the population is excluded from the sample. 1
3 Questions 4 7 are about an experiment in which a fair die is rolled twice. We show the sample space below, with the result on the first shown in white and on the second in gray. 4. Let A denote the event that the sum of the numbers showing on the top faces is 3, and let B denote the event that one of the dice shows 1. Which of the following is true of A and B? a. A B = A. b. A B = A. c. A and B are mutually exclusive. d. All the previous statements are true of A and B. e. None of the previous statements is true of A and B. 2
4 5. Let C denote the event that the first die shows 1, and let D denote the event that one of the dice shows 2. Which of the following is true of C and D? a. C and D are mutually exclusive. b. C and D are independent. c. C D = C. d. C D = D. e. None of the previous statements is true of A and B. 6. Let X denote the sum of the numbers showing on the top faces of the two dice. Which of the the following statements is true of the random variable X? a. X is a discrete random variable with infinitely many values. b. X is a discrete random variable with finitely many values. c. X is a continuous random variable. d. All the previous statements are true of X. e. None of the previous statements is true of X. 7. Let E denote the event that the first die shows 2, and let F denote the event that the sum of the numbers showing on the top faces of the two dice is even. Which of the following is true of the events E and F? a. E F is the event that the second die shows an odd number. b. E F is the event that the second die shows 2. c. E and F are independent events. d. E and F are mutually exclusive events. e. None of the previous statements is true of E and F. 3
5 Questions 8 and 9 are about an analysis of four hundred accidents that occurred on a Saturday night. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown in the table below. Number of Vehicles Involved Totals Did Alcohol Play a Role? or more Totals Yes No Totals Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved more than a single vehicle? a. b. c. d. e Given that an accident involved multiple vehicles, what is the probability that it involved alcohol? a. b. c. d. e Which of the following is a valid probability distribution for a random variable? a. x p(x) b. x p(x) c. x p(x) d. x p(x) e. x p(x)
6 Questions 11 and 12 are about the random variable X, which is equal to the number of lemon meringue pies sold in a day by a local bakery, The Baker s Circle. The bakery has determined a probability distribution for X, which is given by the table below. x p(x) What is the probability that the bakery will sell 7 or more lemon meringue pies in a day? a b c d e What are the expected value E(X) and the standard deviation σ(x) of X? a. E(X) = 1.825, and σ(x) = b. E(X) = 5.517, and σ(x) = c. E(X) = 5.5, and σ(x) = 2.0. d. E(X) = 5.517, and σ(x) = e. None of the above 5
7 Free Response Section Partial credit is possible. Show your work. Unsupported answers might not receive full credit. 13. (12 points) A life insurance company sells a term life insurance policy to a 21yearold male that pays $100,000 if the insured dies within the next 5 years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of $250 each year as payment for the insurance. The amount X that the company earns on this policy is $250 for each year the policy is in force, less the $100,000 that it must pay if the insured dies. Here is the distribution of X. Age at death X $99,750 $99,500 $99,250 $99,000 $98,750 $1250 Probability ? a. Fill in the missing value in the table. b. Find the expected value E(X) of X. c. Find the standard deviation σ(x) of X. d. How many standard deviations from E(X) is the value 0? (The standard deviation is often used as a measure of the risk associated with a financial instrument.) 6
8 14. (14 points) In his novel Bomber, Len Deighton argues that a World War II pilot had a 2% chance of being shot down on each mission. So in 50 missions the pilot is mathematically certain to be shot down, because 50 2% = 100%. Is this a good argument? (Hint: Can you model this situation as a coin tossing experiment? It is allright to make the simplifying assumption that the outcomes of the missions are independent.) 7
9 15. (13 points) Urn A contains 3 red marbles and 2 green marbles, and Urn B contains 2 red marbles and 3 green marbles, A fair coin is tossed. If it turns up heads, a marble is drawn from Urn A, and if it turns up tails, a marble is drawn from Urn B, a. What is the probability that the coin turns up heads? b. Find the probability that a red marble is drawn. c. Find the conditional probability that the coin turns up heads, given that a red marble is drawn. 8
10 16. (13 points) An airline has requests for standby flights at half the usual oneway air fare. Past experience has shown that these passengers have about a 1 in 5 chance of getting on the standby flight. When they fail to get on a flight as a standby, the only other choice is to fly first class on the next flight out. Suppose the usual oneway air fare to a certain city is $148 and the cost of flying first class is $480. Should a passenger who wishes to fly to this city opt to fly as a standby? 9
ACMS 10140 Section 02 Elements of Statistics October 28, 2010 Midterm Examination II Answers
ACMS 10140 Section 02 Elements of Statistics October 28, 2010 Midterm Examination II Answers Name DO NOT remove this answer page. DO turn in the entire exam. Make sure that you have all ten (10) pages
More informationSection 6.2 Definition of Probability
Section 6.2 Definition of Probability Probability is a measure of the likelihood that an event occurs. For example, if there is a 20% chance of rain tomorrow, that means that the probability that it will
More informationMath 150 Sample Exam #2
Problem 1. (16 points) TRUE or FALSE. a. 3 die are rolled, there are 1 possible outcomes. b. If two events are complementary, then they are mutually exclusive events. c. If A and B are two independent
More informationQuestion: What is the probability that a fivecard poker hand contains a flush, that is, five cards of the same suit?
ECS20 Discrete Mathematics Quarter: Spring 2007 Instructor: John Steinberger Assistant: Sophie Engle (prepared by Sophie Engle) Homework 8 Hints Due Wednesday June 6 th 2007 Section 6.1 #16 What is the
More informationExam 3 Review/WIR 9 These problems will be started in class on April 7 and continued on April 8 at the WIR.
Exam 3 Review/WIR 9 These problems will be started in class on April 7 and continued on April 8 at the WIR. 1. Urn A contains 6 white marbles and 4 red marbles. Urn B contains 3 red marbles and two white
More informationContemporary Mathematics MAT 130. Probability. a) What is the probability of obtaining a number less than 4?
Contemporary Mathematics MAT 30 Solve the following problems:. A fair die is tossed. What is the probability of obtaining a number less than 4? What is the probability of obtaining a number less than
More informationBasic concepts in probability. Sue Gordon
Mathematics Learning Centre Basic concepts in probability Sue Gordon c 2005 University of Sydney Mathematics Learning Centre, University of Sydney 1 1 Set Notation You may omit this section if you are
More informationAP Statistics 7!3! 6!
Lesson 64 Introduction to Binomial Distributions Factorials 3!= Definition: n! = n( n 1)( n 2)...(3)(2)(1), n 0 Note: 0! = 1 (by definition) Ex. #1 Evaluate: a) 5! b) 3!(4!) c) 7!3! 6! d) 22! 21! 20!
More informationPROBABILITY NOTIONS. Summary. 1. Random experiment
PROBABILITY NOTIONS Summary 1. Random experiment... 1 2. Sample space... 2 3. Event... 2 4. Probability calculation... 3 4.1. Fundamental sample space... 3 4.2. Calculation of probability... 3 4.3. Non
More informationBasic Probability. Probability: The part of Mathematics devoted to quantify uncertainty
AMS 5 PROBABILITY Basic Probability Probability: The part of Mathematics devoted to quantify uncertainty Frequency Theory Bayesian Theory Game: Playing Backgammon. The chance of getting (6,6) is 1/36.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups
More informationBasic Probability Theory I
A Probability puzzler!! Basic Probability Theory I Dr. Tom Ilvento FREC 408 Our Strategy with Probability Generally, we want to get to an inference from a sample to a population. In this case the population
More informationMath/Stats 425 Introduction to Probability. 1. Uncertainty and the axioms of probability
Math/Stats 425 Introduction to Probability 1. Uncertainty and the axioms of probability Processes in the real world are random if outcomes cannot be predicted with certainty. Example: coin tossing, stock
More informationST 371 (IV): Discrete Random Variables
ST 371 (IV): Discrete Random Variables 1 Random Variables A random variable (rv) is a function that is defined on the sample space of the experiment and that assigns a numerical variable to each possible
More informationSTAT 319 Probability and Statistics For Engineers PROBABILITY. Engineering College, Hail University, Saudi Arabia
STAT 319 robability and Statistics For Engineers LECTURE 03 ROAILITY Engineering College, Hail University, Saudi Arabia Overview robability is the study of random events. The probability, or chance, that
More informationChapter 7 Probability. Example of a random circumstance. Random Circumstance. What does probability mean?? Goals in this chapter
Homework (due Wed, Oct 27) Chapter 7: #17, 27, 28 Announcements: Midterm exams keys on web. (For a few hours the answer to MC#1 was incorrect on Version A.) No grade disputes now. Will have a chance to
More informationChapter 4 Lecture Notes
Chapter 4 Lecture Notes Random Variables October 27, 2015 1 Section 4.1 Random Variables A random variable is typically a realvalued function defined on the sample space of some experiment. For instance,
More informationIntroduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 4.4 Homework
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 4.4 Homework 4.65 You buy a hot stock for $1000. The stock either gains 30% or loses 25% each day, each with probability.
More informationLecture 13. Understanding Probability and LongTerm Expectations
Lecture 13 Understanding Probability and LongTerm Expectations Thinking Challenge What s the probability of getting a head on the toss of a single fair coin? Use a scale from 0 (no way) to 1 (sure thing).
More informationUniversity of California, Los Angeles Department of Statistics. Random variables
University of California, Los Angeles Department of Statistics Statistics Instructor: Nicolas Christou Random variables Discrete random variables. Continuous random variables. Discrete random variables.
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Regular smoker
Exam Chapters 4&5 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) A 28yearold man pays $181 for a oneyear
More informationWorked examples Basic Concepts of Probability Theory
Worked examples Basic Concepts of Probability Theory Example 1 A regular tetrahedron is a body that has four faces and, if is tossed, the probability that it lands on any face is 1/4. Suppose that one
More informationBetting systems: how not to lose your money gambling
Betting systems: how not to lose your money gambling G. Berkolaiko Department of Mathematics Texas A&M University 28 April 2007 / Mini Fair, Math Awareness Month 2007 Gambling and Games of Chance Simple
More information1) The table lists the smoking habits of a group of college students. Answer: 0.218
FINAL EXAM REVIEW Name ) The table lists the smoking habits of a group of college students. Sex Nonsmoker Regular Smoker Heavy Smoker Total Man 5 52 5 92 Woman 8 2 2 220 Total 22 2 If a student is chosen
More informationPROBABILITY 14.3. section. The Probability of an Event
4.3 Probability (43) 727 4.3 PROBABILITY In this section In the two preceding sections we were concerned with counting the number of different outcomes to an experiment. We now use those counting techniques
More informationAMS 5 CHANCE VARIABILITY
AMS 5 CHANCE VARIABILITY The Law of Averages When tossing a fair coin the chances of tails and heads are the same: 50% and 50%. So if the coin is tossed a large number of times, the number of heads and
More information4.1 4.2 Probability Distribution for Discrete Random Variables
4.1 4.2 Probability Distribution for Discrete Random Variables Key concepts: discrete random variable, probability distribution, expected value, variance, and standard deviation of a discrete random variable.
More information+ Section 6.2 and 6.3
Section 6.2 and 6.3 Learning Objectives After this section, you should be able to DEFINE and APPLY basic rules of probability CONSTRUCT Venn diagrams and DETERMINE probabilities DETERMINE probabilities
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 2 Solutions
Math 70/408, Spring 2008 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 2 Solutions About this problem set: These are problems from Course /P actuarial exams that I have collected over the years,
More informationConditional Probability and General Multiplication Rule
Conditional Probability and General Multiplication Rule Objectives:  Identify Independent and dependent events  Find Probability of independent events  Find Probability of dependent events  Find Conditional
More informationSTATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS
STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS 1. If two events (both with probability greater than 0) are mutually exclusive, then: A. They also must be independent. B. They also could
More informationV. RANDOM VARIABLES, PROBABILITY DISTRIBUTIONS, EXPECTED VALUE
V. RANDOM VARIABLES, PROBABILITY DISTRIBUTIONS, EXPETED VALUE A game of chance featured at an amusement park is played as follows: You pay $ to play. A penny and a nickel are flipped. You win $ if either
More informationMath 201: Statistics November 30, 2006
Math 201: Statistics November 30, 2006 Fall 2006 MidTerm #2 Closed book & notes; only an A4size formula sheet and a calculator allowed; 90 mins. No questions accepted! Instructions: There are eleven pages
More informationMA 1125 Lecture 14  Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.
MA 5 Lecture 4  Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the
More informationMind on Statistics. Chapter 8
Mind on Statistics Chapter 8 Sections 8.18.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability that the result
More informationThe number of phone calls to the attendance office of a high school on any given school day A) continuous B) discrete
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) State whether the variable is discrete or continuous.
More informationDetermine the empirical probability that a person selected at random from the 1000 surveyed uses Mastercard.
Math 120 Practice Exam II Name You must show work for credit. 1) A pair of fair dice is rolled 50 times and the sum of the dots on the faces is noted. Outcome 2 4 5 6 7 8 9 10 11 12 Frequency 6 8 8 1 5
More informationStatistics 100A Homework 3 Solutions
Chapter Statistics 00A Homework Solutions Ryan Rosario. Two balls are chosen randomly from an urn containing 8 white, black, and orange balls. Suppose that we win $ for each black ball selected and we
More informationProbability QUESTIONS Principles of Math 12  Probability Practice Exam 1 www.math12.com
Probability QUESTIONS Principles of Math  Probability Practice Exam www.math.com Principles of Math : Probability Practice Exam Use this sheet to record your answers:... 4... 4... 4.. 6. 4.. 6. 7..
More informationJoint Exam 1/P Sample Exam 1
Joint Exam 1/P Sample Exam 1 Take this practice exam under strict exam conditions: Set a timer for 3 hours; Do not stop the timer for restroom breaks; Do not look at your notes. If you believe a question
More informationIntroductory Probability. MATH 107: Finite Mathematics University of Louisville. March 5, 2014
Introductory Probability MATH 07: Finite Mathematics University of Louisville March 5, 204 What is probability? Counting and probability 2 / 3 Probability in our daily lives We see chances, odds, and probabilities
More informationChapter 3 Random Variables and Probability Distributions
Math 322 Probabilit and Statistical Methods Chapter 3 Random Variables and Probabilit Distributions In statistics we deal with random variables variables whose observed value is determined b chance. Random
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Ch.  Problems to look at Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability
More informationQuestion of the Day. Key Concepts. Vocabulary. Mathematical Ideas. QuestionofDay
QuestionofDay Question of the Day What is the probability that in a family with two children, both are boys? What is the probability that in a family with two children, both are boys, if we already know
More informationThe Procedures of Monte Carlo Simulation (and Resampling)
154 Resampling: The New Statistics CHAPTER 10 The Procedures of Monte Carlo Simulation (and Resampling) A Definition and General Procedure for Monte Carlo Simulation Summary Until now, the steps to follow
More informationStatistics and Random Variables. Math 425 Introduction to Probability Lecture 14. Finite valued Random Variables. Expectation defined
Expectation Statistics and Random Variables Math 425 Introduction to Probability Lecture 4 Kenneth Harris kaharri@umich.edu Department of Mathematics University of Michigan February 9, 2009 When a large
More informationChapter 6. 1. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace? Ans: 4/52.
Chapter 6 1. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace? 4/52. 2. What is the probability that a randomly selected integer chosen from the first 100 positive
More informationStatistics 100A Homework 2 Solutions
Statistics Homework Solutions Ryan Rosario Chapter 9. retail establishment accepts either the merican Express or the VIS credit card. total of percent of its customers carry an merican Express card, 6
More informationCh. 13.3: More about Probability
Ch. 13.3: More about Probability Complementary Probabilities Given any event, E, of some sample space, U, of a random experiment, we can always talk about the complement, E, of that event: this is the
More informationMAT 1000. Mathematics in Today's World
MAT 1000 Mathematics in Today's World We talked about Cryptography Last Time We will talk about probability. Today There are four rules that govern probabilities. One good way to analyze simple probabilities
More informationAP Stats  Probability Review
AP Stats  Probability Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. I toss a penny and observe whether it lands heads up or tails up. Suppose
More information2 Elementary probability
2 Elementary probability This first chapter devoted to probability theory contains the basic definitions and concepts in this field, without the formalism of measure theory. However, the range of problems
More informationLesson 1. Basics of Probability. Principles of Mathematics 12: Explained! www.math12.com 314
Lesson 1 Basics of Probability www.math12.com 314 Sample Spaces: Probability Lesson 1 Part I: Basic Elements of Probability Consider the following situation: A six sided die is rolled The sample space
More information4.3. Addition and Multiplication Laws of Probability. Introduction. Prerequisites. Learning Outcomes. Learning Style
Addition and Multiplication Laws of Probability 4.3 Introduction When we require the probability of two events occurring simultaneously or the probability of one or the other or both of two events occurring
More informationPaper No 19. FINALTERM EXAMINATION Fall 2009 MTH302 Business Mathematics & Statistics (Session  2) Ref No: Time: 120 min Marks: 80
Paper No 19 FINALTERM EXAMINATION Fall 2009 MTH302 Business Mathematics & Statistics (Session  2) Ref No: Time: 120 min Marks: 80 Question No: 1 ( Marks: 1 )  Please choose one Scatterplots are used
More informationP(X = x k ) = 1 = k=1
74 CHAPTER 6. IMPORTANT DISTRIBUTIONS AND DENSITIES 6.2 Problems 5.1.1 Which are modeled with a unifm distribution? (a Yes, P(X k 1/6 f k 1,...,6. (b No, this has a binomial distribution. (c Yes, P(X k
More informationMATHEMATICS FOR ENGINEERS STATISTICS TUTORIAL 4 PROBABILITY DISTRIBUTIONS
MATHEMATICS FOR ENGINEERS STATISTICS TUTORIAL 4 PROBABILITY DISTRIBUTIONS CONTENTS Sample Space Accumulative Probability Probability Distributions Binomial Distribution Normal Distribution Poisson Distribution
More informationProbability: Terminology and Examples Class 2, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Probability: Terminology and Examples Class 2, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Know the definitions of sample space, event and probability function. 2. Be able to
More informationProbability OPRE 6301
Probability OPRE 6301 Random Experiment... Recall that our eventual goal in this course is to go from the random sample to the population. The theory that allows for this transition is the theory of probability.
More informationSecond Midterm Exam (MATH1070 Spring 2012)
Second Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notecard. Calculators are allowed, but other electronics are prohibited. 1. [60pts] Multiple Choice Problems
More informationSTAT 35A HW2 Solutions
STAT 35A HW2 Solutions http://www.stat.ucla.edu/~dinov/courses_students.dir/09/spring/stat35.dir 1. A computer consulting firm presently has bids out on three projects. Let A i = { awarded project i },
More informationChapter 4. Probability Distributions
Chapter 4 Probability Distributions Lesson 41/42 Random Variable Probability Distributions This chapter will deal the construction of probability distribution. By combining the methods of descriptive
More informationMathematics of Risk. Introduction. Case Study #1 Personal Auto Insurance Pricing. Mathematical Concepts Illustrated. Background
Mathematics of Risk Introduction There are many mechanisms that individuals and organizations use to protect themselves against the risk of financial loss. Government organizations and public and private
More informationReview for Test 2. Chapters 4, 5 and 6
Review for Test 2 Chapters 4, 5 and 6 1. You roll a fair sixsided die. Find the probability of each event: a. Event A: rolling a 3 1/6 b. Event B: rolling a 7 0 c. Event C: rolling a number less than
More informationName: Math 29 Probability. Practice Second Midterm Exam 1. 1. Show all work. You may receive partial credit for partially completed problems.
Name: Math 29 Probability Practice Second Midterm Exam 1 Instructions: 1. Show all work. You may receive partial credit for partially completed problems. 2. You may use calculators and a onesided sheet
More informationThe Binomial Probability Distribution
The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Objectives After this lesson we will be able to: determine whether a probability
More informationConcepts of Probability
Concepts of Probability Trial question: we are given a die. How can we determine the probability that any given throw results in a six? Try doing many tosses: Plot cumulative proportion of sixes Also look
More informationSample Questions for Mastery #5
Name: Class: Date: Sample Questions for Mastery #5 Multiple Choice Identify the choice that best completes the statement or answers the question.. For which of the following binomial experiments could
More informationTHE MULTINOMIAL DISTRIBUTION. Throwing Dice and the Multinomial Distribution
THE MULTINOMIAL DISTRIBUTION Discrete distribution  The Outcomes Are Discrete. A generalization of the binomial distribution from only 2 outcomes to k outcomes. Typical Multinomial Outcomes: red A area1
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Exam Name 1) Solve the system of linear equations: 2x + 2y = 1 3x  y = 6 2) Consider the following system of linear inequalities. 5x + y 0 5x + 9y 180 x + y 5 x 0, y 0 1) 2) (a) Graph the feasible set
More informationSTAB47S:2003 Midterm Name: Student Number: Tutorial Time: Tutor:
STAB47S:200 Midterm Name: Student Number: Tutorial Time: Tutor: Time: 2hours Aids: The exam is open book Students may use any notes, books and calculators in writing this exam Instructions: Show your reasoning
More informationMAS108 Probability I
1 QUEEN MARY UNIVERSITY OF LONDON 2:30 pm, Thursday 3 May, 2007 Duration: 2 hours MAS108 Probability I Do not start reading the question paper until you are instructed to by the invigilators. The paper
More informationBasic Probability Theory II
RECAP Basic Probability heory II Dr. om Ilvento FREC 408 We said the approach to establishing probabilities for events is to Define the experiment List the sample points Assign probabilities to the sample
More informationSTATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4
STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate
More informationMathematical Expectation
Mathematical Expectation Properties of Mathematical Expectation I The concept of mathematical expectation arose in connection with games of chance. In its simplest form, mathematical expectation is the
More informationFind an expected value involving two events. Find an expected value involving multiple events. Use expected value to make investment decisions.
374 Chapter 8 The Mathematics of Likelihood 8.3 Expected Value Find an expected value involving two events. Find an expected value involving multiple events. Use expected value to make investment decisions.
More informationSection 5 Part 2. Probability Distributions for Discrete Random Variables
Section 5 Part 2 Probability Distributions for Discrete Random Variables Review and Overview So far we ve covered the following probability and probability distribution topics Probability rules Probability
More informationFEGYVERNEKI SÁNDOR, PROBABILITY THEORY AND MATHEmATICAL
FEGYVERNEKI SÁNDOR, PROBABILITY THEORY AND MATHEmATICAL STATIsTICs 4 IV. RANDOm VECTORs 1. JOINTLY DIsTRIBUTED RANDOm VARIABLEs If are two rom variables defined on the same sample space we define the joint
More informationSolution. Solution. (a) Sum of probabilities = 1 (Verify) (b) (see graph) Chapter 4 (Sections 4.34.4) Homework Solutions. Section 4.
Math 115 N. Psomas Chapter 4 (Sections 4.34.4) Homework s Section 4.3 4.53 Discrete or continuous. In each of the following situations decide if the random variable is discrete or continuous and give
More informationWHERE DOES THE 10% CONDITION COME FROM?
1 WHERE DOES THE 10% CONDITION COME FROM? The text has mentioned The 10% Condition (at least) twice so far: p. 407 Bernoulli trials must be independent. If that assumption is violated, it is still okay
More informationA probability experiment is a chance process that leads to welldefined outcomes. 3) What is the difference between an outcome and an event?
Ch 4.2 pg.191~(110 all), 12 (a, c, e, g), 13, 14, (a, b, c, d, e, h, i, j), 17, 21, 25, 31, 32. 1) What is a probability experiment? A probability experiment is a chance process that leads to welldefined
More informationAn Introduction to Basic Statistics and Probability
An Introduction to Basic Statistics and Probability Shenek Heyward NCSU An Introduction to Basic Statistics and Probability p. 1/4 Outline Basic probability concepts Conditional probability Discrete Random
More informationChapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions.
Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More informationMath 3C Homework 3 Solutions
Math 3C Homework 3 s Ilhwan Jo and Akemi Kashiwada ilhwanjo@math.ucla.edu, akashiwada@ucla.edu Assignment: Section 2.3 Problems 2, 7, 8, 9,, 3, 5, 8, 2, 22, 29, 3, 32 2. You draw three cards from a standard
More informationnumber of favorable outcomes total number of outcomes number of times event E occurred number of times the experiment was performed.
12 Probability 12.1 Basic Concepts Start with some Definitions: Experiment: Any observation of measurement of a random phenomenon is an experiment. Outcomes: Any result of an experiment is called an outcome.
More informationChapter 5 A Survey of Probability Concepts
Chapter 5 A Survey of Probability Concepts True/False 1. Based on a classical approach, the probability of an event is defined as the number of favorable outcomes divided by the total number of possible
More informationElementary Statistics and Inference. Elementary Statistics and Inference. 16 The Law of Averages (cont.) 22S:025 or 7P:025.
Elementary Statistics and Inference 22S:025 or 7P:025 Lecture 20 1 Elementary Statistics and Inference 22S:025 or 7P:025 Chapter 16 (cont.) 2 D. Making a Box Model Key Questions regarding box What numbers
More informationLesson 1: Experimental and Theoretical Probability
Lesson 1: Experimental and Theoretical Probability Probability is the study of randomness. For instance, weather is random. In probability, the goal is to determine the chances of certain events happening.
More informationRANDOM VARIABLES MATH CIRCLE (ADVANCED) 3/3/2013. 3 k) ( 52 3 )
RANDOM VARIABLES MATH CIRCLE (ADVANCED) //0 0) a) Suppose you flip a fair coin times. i) What is the probability you get 0 heads? ii) head? iii) heads? iv) heads? For = 0,,,, P ( Heads) = ( ) b) Suppose
More informationProbability, statistics and football Franka Miriam Bru ckler Paris, 2015.
Probability, statistics and football Franka Miriam Bru ckler Paris, 2015 Please read this before starting! Although each activity can be performed by one person only, it is suggested that you work in groups
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 0.4987 B) 0.9987 C) 0.0010 D) 0.
Ch. 5 Normal Probability Distributions 5.1 Introduction to Normal Distributions and the Standard Normal Distribution 1 Find Areas Under the Standard Normal Curve 1) Find the area under the standard normal
More informationHomework 8 Solutions
CSE 21  Winter 2014 Homework Homework 8 Solutions 1 Of 330 male and 270 female employees at the Flagstaff Mall, 210 of the men and 180 of the women are on flextime (flexible working hours). Given that
More informationMATH 140 Lab 4: Probability and the Standard Normal Distribution
MATH 140 Lab 4: Probability and the Standard Normal Distribution Problem 1. Flipping a Coin Problem In this problem, we want to simualte the process of flipping a fair coin 1000 times. Note that the outcomes
More informationLet U = {Sun., Mon., Tue., Wed., Thur., Fri., Sat.} A = {Mon., Wed., Fri., Sat.}
MATH 102 Final Exam Practice Fall 2012 Use the information below to answer questions 14. Let U = {Sun., Mon., Tue., Wed., Thur., Fri., Sat.} A = {Mon., Wed., Fri., Sat.} B = {Sat., Sun.} C = {Tue., Wed.,
More informationIn the situations that we will encounter, we may generally calculate the probability of an event
What does it mean for something to be random? An event is called random if the process which produces the outcome is sufficiently complicated that we are unable to predict the precise result and are instead
More informationStats Review Chapters 56
Stats Review Chapters 56 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test
More informationDefinition and Calculus of Probability
In experiments with multivariate outcome variable, knowledge of the value of one variable may help predict another. For now, the word prediction will mean update the probabilities of events regarding the
More informationhttps://assessment.casa.uh.edu/assessment/printtest.htm PRINTABLE VERSION Quiz 10
1 of 8 4/9/2013 8:17 AM PRINTABLE VERSION Quiz 10 Question 1 Let A and B be events in a sample space S such that P(A) = 0.34, P(B) = 0.39 and P(A B) = 0.19. Find P(A B). a) 0.4872 b) 0.5588 c) 0.0256 d)
More informationFeb 7 Homework Solutions Math 151, Winter 2012. Chapter 4 Problems (pages 172179)
Feb 7 Homework Solutions Math 151, Winter 2012 Chapter Problems (pages 172179) Problem 3 Three dice are rolled. By assuming that each of the 6 3 216 possible outcomes is equally likely, find the probabilities
More information