SAMPLE PROBLEM PROBLEM SET - EXAM P/CAS 1
|
|
- Ernest Thomas
- 5 years ago
- Views:
Transcription
1 SAMPLE PROBLEM SET - EXAM P/CAS 1 1 SAMPLE PROBLEM PROBLEM SET - EXAM P/CAS 1 1. A life insurer classifies insurance applicants according to the folloing attributes: Q - the applicant is male L - the applicant is a homeoner Out of a large number of applicants the insurer has identified the folloing information: 40% of applicants are male, 40% of applicants are homeoners and 20% of applicants are female homeoners. Find the percentage of applicants ho are male and do not on a home. A.1 B.2 C.3 D.4 E.5 2. A test for a disease correctly diagnoses a diseased person as having the disease ith probability.85. The test incorrectly diagnoses someone ithout the disease as having the disease ith a probability of.10. If 1% of the people in a population have the disease, hat is the chance that a person from this population ho tests positive for the disease actually has the disease? A!!& B!( C!(& D &!! E!!! 3. A class contains 8 boys and 7 girls. The teacher selects 3 of the children at random and ithout replacement. Calculate the probability that number of boys selected exceeds the number of girls selected. & &' $' A $$(& B '& C & D $$(& E '& B 4. \ is a continuous random variable ith density function 0ÐBÑ œ -/ ß B. Find TÒ\ $l\ Ó. $ A / B / C / D / / E / / 5. To players put one dollar into a pot. They decide to thro a pair of dice alternately. The first one ho thros a total of 5 on both dice ins the pot. Ho much should the player ho starts add to the pot to make this a fair game? A B C D E
2 2 SAMPLE PROBLEM SET - EXAM P/CAS 1 6. A carnival sharpshooter game charges $25 for 25 shots at a target. If the shooter hits the bullseye feer than 5 times then he gets no prize. If he hits the bullseye 5 times he gets back $10. For each additional bullseye over 5 he gets back an additional $5. The shooter estimates that he has a.2 probability of hitting the bullseye on any given shot. What is the shooter's expected gain if he plays the game (nearest $1? A & B! C & D! E & 7. Three individuals are running a one kilometer race. The completion time for each individual is a random variable. \ 3 is the completion time, in minutes, for person 3. \ À uniform distribution on the interval Ò ß $Ó \ À uniform distribution on the interval Ò( ß $Ó \ $ À uniform distribution on the interval Ò ß $$Ó The three completion times are independent of one another. Find the probability that the earliest completion time is less than 3 minutes. A.89 B.91 C.94 D.96 E Let \ and ] be continuous random variables ith joint density function BC for!ÿbÿ and!ÿcÿ \ 0ÐBßCÑ œ š. What is TÒ Ÿ ] Ÿ \Ó!ß otherise? $ $ $ A $ B C % D E % 9. Bob and Doug are both 100-metre sprinters. Bob's sprint time is normally distributed ith a mean of seconds and Doug's sprint time is also normally distributed, but ith a mean of 9.90 seconds. Both have the same standard deviation in sprint time of 5. Assuming that Bob and Doug have independent sprint times, and given that there is.& chance that Doug beats Bob in any given race, find 5. A.040 B.041 C.042 D.043 E A loss random variable is uniformly distributed on the integers from 0 to 11. An insurance pays the loss in excess of a deductible of 5.5. Find the expected amount not covered by the insurance. A 2 B 3 C 4 D 5 E 6
3 SAMPLE PROBLEM SET - EXAM P/CAS 1 3 SAMPLE PROBLEM PROBLEM SET SOLUTIONS 1. TÒQÓ œ %ß TÒQ Ó œ 'ß TÒLÓ œ %ß TÒL Ó œ 'ß TÒQ LÓ œ ß We ish to find TÒQ L Ó. From probability rules, e have ' œ T ÒL Ó œ T ÒQ L Ó T ÒQ L Ó, and ' œ T ÒQ Ó œ T ÒQ LÓ T ÒQ L Ó œ T ÒQ L Ó. Thus, T ÒQ L Ó œ % and then T ÒQ L Ó œ. The folloing diagram identifies the component probabilities. The calculations above can also be summarized in the folloing table. The events across the top of the table categorize individuals as male ( Q or female ( Q, and the events don the left side of the table categorize individuals as homeoners ( L or non-homeoners ( L. TÐQÑœ%, given TÐQÑœ %œ' TÐLÑ œ % TÐQ LÑ É TÐQ LÑ œ, given given TÐLÑœ %œ' Anser: B œtðlñ TÐQ LÑœ% œ TÐQ LÑœTÐQÑ TÐQ LÑœ% œ 2. We define the folloing events: H - a person has the disease, XT - a person tests positive for the disease. We are given TÒXTlHÓ œ & and T ÒX T lh Ó œ! and T ÒHÓ œ!. We ish to find T ÒHlX T Ó. Using the formulation for conditional probability e have TÒHlXTÓ œ TÒH XTÓ TÒXTÓ. But T ÒH X T Ó œ T ÒX T lhó T ÒHÓ œ Ð&ÑÐ!Ñ œ!!&, and T ÒH X T Ó œ T ÒX T lh Ó T ÒH Ó œ Ð!ÑÐÑ œ!. Then,!!& T ÒX T Ó œ T ÒH X T Ó T ÒH X T Ó œ!(& p T ÒHlX T Ó œ!(& œ!(.
4 4 SAMPLE PROBLEM SET - EXAM P/CAS 1 2. continued The folloing table summarizes the calculations. TÒHÓ œ!, given Ê TÒH Ó œ TÒHÓ œ TÒH XTÓ œ T ÒX T lhó T ÒHÓ œ!!& T ÒX T Ó œ T ÒH X T Ó T ÒH X T Ó œ!(& TÒH XTÓ œ T ÒX T lh Ó T ÒH Ó œ! TÒH XTÓ!!& T ÒHlX T Ó œ TÒXTÓ œ!(& œ!(. Anser: B & &x & % $ 3. There are Œ œ œ œ %&& ays of selecting $ children from a group of $ $x x $ & ithout replacement. The number of boys selected exceeds the number of girls selected if either (i $ boys and! girls are selected, or (ii boys and girl are selected. ( There are Œ Œ ays in hich selection (i can occur, and $! œ x (x $x &x!x (x œ &' ( there are Œ Œ ays in hich selection (ii can occur. œ x (x x 'x x 'x œ ' &' ' $' The probability of either (i or (ii occurring is %&& œ '& Anser: E T Ò \ $Ó 4. TÒ\ $l\ Óœ TÒ\ Ó TÒ\ Ó œ ' B -/.B œ -/ TÒ \ $Ó œ ' $ B $, -/.B œ -Ð/ / Ñß $ -Ð/ / Ñ TÒ\ $l\ Óœ -/ œ /. Note that e can find -, from œ ' 0ÐBÑ.B œ ' -/ B.B œ -/ p - œ / ; but this is not necessary for this exercise. Anser: A
5 SAMPLE PROBLEM SET - EXAM P/CAS Player 1 thros the dice on thros 1, 3, 5,... and the probability that player ins on thro 5 is Ð for 5 œ!ßßß$ß (there is a probability of throing a total of 5 on any 5 one thro of the pair of dice. The probability that player 1 ins the pot is % ✠œ Ñ Player 2 thros the dice on thros 2, 4, 6,.. The probability that player 2 ins the pot on thro 5 is Ð Ñ 5 for 5 œßß$ßand the probability that player 2 ins is 1 $ 1 & 1 1 â œ œ œ Ñ If player 1 puts - dollars into the pot, then his expected gain is -Ñ and player 2's expected gain is Ð -Ñ In order for the to players to have the same expected gain, e must have -Ñ œ!, so that -œ Anser: C 6. No. of bullseyes:! $ % & ' ( & Prize:!!!!!! &!! &\ & À &! &! &! &!! Let \œ number of bullseyes. \ has a binomial distribution ith 8œ&, :œ, and & B & B IÒ\Ó œ &. :ÐBÑ œ Š B ÐÑ ÐÑ Note that for 5 bullseyes or more the prize is &\ &. We can find the expected prize by first finding IÒ&\ &Ó and adjusting for the factors corresponding to \ œ!ß ß ß $ß % Therefore, Expected prize œ IÒ&\ &Ó & :Ð!Ñ! :ÐÑ & :ÐÑ! :Ð$Ñ &:Ð%Ñ &! & & % & $ œ &IÒ\Ó & & Š! ÐÑ ÐÑ! Š ÐÑÐÑ & Š ÐÑ ÐÑ & $ & % Ð!ÑŠ $ ÐÑ ÐÑ & Š % ÐÑ ÐÑ œ (. The expected gain is ( & œ &. 7. 0\ Ð>Ñœ œ& for Ÿ>Ÿ$ß J\ Ð>ÑœTÒ\ Ÿ>Óœ&Ð> Ñ for Ÿ>Ÿ$ 0\ Ð>Ñ œ œ & Ÿ > Ÿ $ ß J\ Ð>Ñ œ T Ò\ Ÿ >Ó œ &Ð> (Ñ ( Ÿ > Ÿ $ for 7 for 2 0\ $ Ð>Ñ œ % œ & for Ÿ > Ÿ $$ ß J\ $ Ð>Ñ œ T Ò\ $ Ÿ >Ó œ &Ð> Ñ for Ÿ > Ÿ $$ TÒ738Ð\ß\ß\Ñ $Óœ TÒ738Ð\ß\ß\Ñ $ $ $Ó œ TÒÐ\ $Ñ Ð\ $Ñ Ð\ $ $ÑÓ œ Ò J\ Ð$ÑÓ Ò J\ Ð$ÑÓ Ò J\ $ Ð$ÑÓ œ Ò &Ð$ ÑÓ Ò &Ð$ (ÑÓ Ò &Ð$ ÑÓ œ!'&. Anser: B
6 6 SAMPLE PROBLEM SET - EXAM P/CAS 1 8. The region of probability is shon in the shaded figure belo The probability is ' ' B ' ' $ $! BÎ BC.C.B BÎ BC.C.B œ $ $ œ. Alternatively, the probability is ' ' C! C BC.B.C œ œ $. Anser: D 9. F HµRÐß 5 F H! ÑTÒF HÓœTÒF H!ÓœTÒ Óœ& 5È 5È! Ê œ '%& T Ò^ '%&Ó œ & p œ!%$ 5 È (since 5. Anser: D 10. The amount not covered is Loss! $ % & ' ( â Amt.! $ % & && && â && Not Covered Prob. â The expected amount not covered by the insurance is Ð ÑÒ! $ % & &&Ð'ÑÓœ%. Anser: C
CREDIBILITY - PROBLEM SET 1 Limited Fluctuation Credibility
CREDIBILITY PROBLEM SET 1 Limited Fluctuation Credibility 1 The criterion for the number of exposures needed for full credibility is changed from requiring \ to be ithin IÒ\Ó ith probability Þ*, to requiring
More informationSIMULATION - PROBLEM SET 2
SIMULATION - PROBLEM SET Problems 1 to refer the following random sample of 15 data points: 8.0, 5.1,., 8.6, 4.5, 5.6, 8.1, 6.4,., 7., 8.0, 4.0, 6.5, 6., 9.1 The following three bootstrap samples of the
More informationACTEX. SOA Exam STAM Study Manual. With StudyPlus + Spring 2018 Edition Volume I Samuel A. Broverman, Ph.D., ASA
ACTEX SOA Exam STAM Study Manual With StudyPlus + StudyPlus + gives you digital access* to: Actuarial Exam & Career Strategy Guides Technical Skill elearning Tools Samples of Supplemental Textbooks And
More informationMyMathLab Homework: 11. Section 12.1 & 12.2 Derivatives and the Graph of a Function
DERIVATIVES AND FUNCTION GRAPHS Text References: Section " 2.1 & 12.2 MyMathLab Homeork: 11. Section 12.1 & 12.2 Derivatives and the Graph of a Function By inspection of the graph of the function, e have
More informationTABLE OF CONTENTS - VOLUME 1
TABLE OF CONTENTS - VOLUME 1 INTRODUCTORY COMMENTS MODELING SECTION 1 - PROBABILITY REVIE PROBLEM SET 1 LM-1 LM-9 SECTION 2 - REVIE OF RANDOM VARIABLES - PART I PROBLEM SET 2 LM-19 LM-29 SECTION 3 - REVIE
More informationMath 1AA3/1ZB3 Sample Test 1, Version #1
Math 1AA3/1ZB3 Sample Test 1, Version 1 Name: (Last Name) (First Name) Student Number: Tutorial Number: This test consists of 20 multiple choice questions worth 1 mark each (no part marks), and 1 question
More informationMAY 2007 SOA EXAM MLC SOLUTIONS
1 : œ : : p : œ Þ*& ( ( ( ( Þ*' (& ' B Þ( %:( œ / ( B œ / Þ*& Þ( & ( ( % ( MAY 2007 SOA EXAM MLC SOLUTIONS : œ : : œ Þ*' / œ Þ))* Answer: E 2 Z+
More informationAnomalies and monotonicity in net present value calculations
Anomalies and monotonicity in net present value calculations Marco Lonzi and Samuele Riccarelli * Dipartimento di Metodi Quantitativi Università degli Studi di Siena P.zza San Francesco 14 53100 Siena
More informationS. BROVERMAN STUDY GUIDE FOR THE SOCIETY OF ACTUARIES EXAM MLC 2010 EDITION EXCERPTS. Samuel Broverman, ASA, PHD
S BROVERMAN STUDY GUIDE FOR THE SOCIETY OF ACTUARIES EXAM MLC 2010 EDITION EXCERPTS Samuel Broverman, ASA, PHD 2brove@rogerscom wwwsambrovermancom copyright 2010, S Broverman Excerpts: Table of Contents
More informationACT455H1S - TEST 1 - FEBRUARY 6, 2007
ACT455H1S - TEST 1 - FEBRUARY 6, 2007 Write name and student number on each page. Write your solution for each question in the space provided. For the multiple decrement questions, it is always assumed
More informationNOVEMBER 2003 SOA COURSE 3 EXAM SOLUTIONS
NOVEMER 2003 SOA COURSE 3 EXAM SOLUTIONS Prepared by Sam roverman http://membersrogerscom/2brove 2brove@rogerscom sam@utstattorontoedu 1 l; $!À$ œ $ ; $!À$ ; $!À$ œ $ ; $! $ ; $ ; $! ; $ (the second equality
More informationc. What is the probability that the next car tuned has at least six cylinders? More than six cylinders?
Exercises Section 3.2 [page 98] 11. An automobile service facility specializing in engine tune-ups knows that %&% of all tune-ups are done on four-cylinder automobiles, %!% on six-cylinder automobiles,
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 informationS. BROVERMAN STUDY GUIDE FOR THE SOCIETY OF ACTUARIES EXAM MLC 2012 EDITION EXCERPTS. Samuel Broverman, ASA, PHD
S. ROVERMAN STUDY GUIDE FOR THE SOCIETY OF ACTUARIES EXAM MLC 2012 EDITION EXCERPTS Samuel roverman, ASA, PHD 2brove@rogers.com www.sambroverman.com copyright 2012, S. roverman www.sambroverman.com SOA
More informationReview for Exam 2. item to the quantity sold BÞ For which value of B will the corresponding revenue be a maximum?
Review for Exam 2.) Suppose we are given the demand function :œ& % ß where : is the unit price and B is the number of units sold. Recall that the revenue function VÐBÑ œ B:Þ (a) Find the revenue function
More informationLOAN DEBT ANALYSIS (Developed, Composed & Typeset by: J B Barksdale Jr / )
LOAN DEBT ANALYSIS (Developed, Composed & Typeset by: J B Barksdale Jr / 06 04 16) Article 01.: Loan Debt Modelling. Instances of a Loan Debt arise whenever a Borrower arranges to receive a Loan from a
More information1. The probability that a visit to a primary care physician s (PCP) office results in neither
1. The probability that a visit to a primary care physician s (PCP) office results in neither lab work nor referral to a specialist is 35%. Of those coming to a PCP s office, 30% are referred to specialists
More informationFirst Exam for MTH 23
First Exam for MTH 23 October 5, 2017 Nikos Apostolakis Name: Instructions: This exam contains 6 pages (including this cover page) and 5 questions. Each question is worth 20 points, and so the perfect
More information6.042/18.062J Mathematics for Computer Science November 30, 2006 Tom Leighton and Ronitt Rubinfeld. Expected Value I
6.42/8.62J Mathematics for Computer Science ovember 3, 26 Tom Leighton and Ronitt Rubinfeld Lecture otes Expected Value I The expectation or expected value of a random variable is a single number that
More informationName Period AP Statistics Unit 5 Review
Name Period AP Statistics Unit 5 Review Multiple Choice 1. Jay Olshansky from the University of Chicago was quoted in Chance News as arguing that for the average life expectancy to reach 100, 18% of people
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 informationCentral Limit Theorem, Joint Distributions Spring 2018
Central Limit Theorem, Joint Distributions 18.5 Spring 218.5.4.3.2.1-4 -3-2 -1 1 2 3 4 Exam next Wednesday Exam 1 on Wednesday March 7, regular room and time. Designed for 1 hour. You will have the full
More informationBinomial formulas: The binomial coefficient is the number of ways of arranging k successes among n observations.
Chapter 8 Notes Binomial and Geometric Distribution Often times we are interested in an event that has only two outcomes. For example, we may wish to know the outcome of a free throw shot (good or missed),
More informationName: CS3130: Probability and Statistics for Engineers Practice Final Exam Instructions: You may use any notes that you like, but no calculators or computers are allowed. Be sure to show all of your work.
More informationPrecise Frequency and Amplitude Tracking of Waveforms CFS-175 Web Version August 30 through October 24, 1999
Precise Frequency and Amplitude Tracking of Waveforms CFS-175 We Version August 30 through Octoer 2, 1999 David Dunthorn.c-f-systems.com Note This document has een assemled from the major parts of three
More informationSOCIETY OF ACTUARIES EXAM STAM SHORT-TERM ACTUARIAL MATHEMATICS EXAM STAM SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM STAM SHORT-TERM ACTUARIAL MATHEMATICS EXAM STAM SAMPLE QUESTIONS Questions 1-307 have been taken from the previous set of Exam C sample questions. Questions no longer relevant
More informationCHAPTER 6 Random Variables
CHAPTER 6 Random Variables 6.3 Binomial and Geometric Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Binomial and Geometric Random
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 informationAP Statistics Section 6.1 Day 1 Multiple Choice Practice. a) a random variable. b) a parameter. c) biased. d) a random sample. e) a statistic.
A Statistics Section 6.1 Day 1 ultiple Choice ractice Name: 1. A variable whose value is a numerical outcome of a random phenomenon is called a) a random variable. b) a parameter. c) biased. d) a random
More informationPROBABILITY DISTRIBUTIONS
CHAPTER 3 PROBABILITY DISTRIBUTIONS Page Contents 3.1 Introduction to Probability Distributions 51 3.2 The Normal Distribution 56 3.3 The Binomial Distribution 60 3.4 The Poisson Distribution 64 Exercise
More informationApplied Mathematics 12 Extra Practice Exercises Chapter 3
H E LP Applied Mathematics Extra Practice Exercises Chapter Tutorial., page 98. A bag contains 5 red balls, blue balls, and green balls. For each of the experiments described below, complete the given
More information1. For a special whole life insurance on (x), payable at the moment of death:
**BEGINNING OF EXAMINATION** 1. For a special whole life insurance on (x), payable at the moment of death: µ () t = 0.05, t > 0 (ii) δ = 0.08 x (iii) (iv) The death benefit at time t is bt 0.06t = e, t
More information3. The Dynamic Programming Algorithm (cont d)
3. The Dynamic Programming Algorithm (cont d) Last lecture e introduced the DPA. In this lecture, e first apply the DPA to the chess match example, and then sho ho to deal ith problems that do not match
More informationSection 6.3 Binomial and Geometric Random Variables
Section 6.3 Binomial and Geometric Random Variables Mrs. Daniel AP Stats Binomial Settings A binomial setting arises when we perform several independent trials of the same chance process and record the
More informationIn a binomial experiment of n trials, where p = probability of success and q = probability of failure. mean variance standard deviation
Name In a binomial experiment of n trials, where p = probability of success and q = probability of failure mean variance standard deviation µ = n p σ = n p q σ = n p q Notation X ~ B(n, p) The probability
More informationReview. What is the probability of throwing two 6s in a row with a fair die? a) b) c) d) 0.333
Review In most card games cards are dealt without replacement. What is the probability of being dealt an ace and then a 3? Choose the closest answer. a) 0.0045 b) 0.0059 c) 0.0060 d) 0.1553 Review What
More information9.2 Adverse Selection under Certainty: Lemons I and II. The principal contracts to buy from the agent a car whose quality
9.2 Adverse Selection under Certainty: Lemons I and II The principal contracts to buy from the agent a car whose quality is noncontractible despite the lack of uncertainty. The Basic Lemons Model ð Players
More informationBinomial Random Variable - The count X of successes in a binomial setting
6.3.1 Binomial Settings and Binomial Random Variables What do the following scenarios have in common? Toss a coin 5 times. Count the number of heads. Spin a roulette wheel 8 times. Record how many times
More informationACT370H1S - TEST 2 - MARCH 25, 2009
ACT370H1S - TEST 2 - MARCH 25, 2009 Write name and student number on each page. Write your solution for each question in the space provided. Do all calculations to at least 6 significant figures. The only
More informationSTT 315 Practice Problems Chapter 3.7 and 4
STT 315 Practice Problems Chapter 3.7 and 4 Answer the question True or False. 1) The number of children in a family can be modelled using a continuous random variable. 2) For any continuous probability
More informationEcon 101A Midterm 2 Th 6 November 2003.
Econ 101A Midterm 2 Th 6 November 2003. You have approximately 1 hour and 20 minutes to anser the questions in the midterm. I ill collect the exams at 12.30 sharp. Sho your k, and good luck! Problem 1.
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 informationSTAT 3090 Test 2 - Version B Fall Student s Printed Name: PLEASE READ DIRECTIONS!!!!
Student s Printed Name: Instructor: XID: Section #: Read each question very carefully. You are permitted to use a calculator on all portions of this exam. You are NOT allowed to use any textbook, notes,
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 informationCREDIBILITY - PROBLEM SET 2 Bayesian Analysis - Discrete Prior
CREDIBILITY - PROBLEM SET 2 Bayesian Analysis - Discrete Prior Questions 1 and 2 relate to the following situation Two bowls each contain 10 similarly shaped balls Bowl 1 contains 5 red and 5 white balls
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 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 information3. The n observations are independent. Knowing the result of one observation tells you nothing about the other observations.
Binomial and Geometric Distributions - Terms and Formulas Binomial Experiments - experiments having all four conditions: 1. Each observation falls into one of two categories we call them success or failure.
More informationName: 1332 Review for Final. 1. Use the given definitions to answer the following questions. 1,2,3,4,5,6,7,8,9,10
1 Name: 1332 Review for Final 1. Use the given definitions to answer the following questions. U E A B C 1,2,3,4,5,6,7,8,9,10 x x is even 1,2,4,7,8 1,3, 4,5,8 2,4,8 D x x is a power of 2 and 2 x 10 a. Is
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 informationList of Online Quizzes: Quiz7: Basic Probability Quiz 8: Expectation and sigma. Quiz 9: Binomial Introduction Quiz 10: Binomial Probability
List of Online Homework: Homework 6: Random Variables and Discrete Variables Homework7: Expected Value and Standard Dev of a Variable Homework8: The Binomial Distribution List of Online Quizzes: Quiz7:
More 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 informationMATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - SUMMER DR. DAVID BRIDGE
MATH 2053 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - SUMMER 2007 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the
More informationSTAT 1220 FALL 2010 Common Final Exam December 10, 2010
STAT 1220 FALL 2010 Common Final Exam December 10, 2010 PLEASE PRINT THE FOLLOWING INFORMATION: Name: Instructor: Student ID #: Section/Time: THIS EXAM HAS TWO PARTS. PART I. Part I consists of 30 multiple
More informationThe Binomial and Geometric Distributions. Chapter 8
The Binomial and Geometric Distributions Chapter 8 8.1 The Binomial Distribution A binomial experiment is statistical experiment that has the following properties: The experiment consists of n repeated
More information3. The n observations are independent. Knowing the result of one observation tells you nothing about the other observations.
Binomial and Geometric Distributions - Terms and Formulas Binomial Experiments - experiments having all four conditions: 1. Each observation falls into one of two categories we call them success or failure.
More informationRandom Variables. Chapter 6: Random Variables 2/2/2014. Discrete and Continuous Random Variables. Transforming and Combining Random Variables
Chapter 6: Random Variables Section 6.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Random Variables 6.1 6.2 6.3 Discrete and Continuous Random Variables Transforming and Combining
More informationChapter 7. Random Variables
Chapter 7 Random Variables Making quantifiable meaning out of categorical data Toss three coins. What does the sample space consist of? HHH, HHT, HTH, HTT, TTT, TTH, THT, THH In statistics, we are most
More informationChapter 7. Random Variables: 7.1: Discrete and Continuous. Random Variables. 7.2: Means and Variances of. Random Variables
Chapter 7 Random Variables In Chapter 6, we learned that a!random phenomenon" was one that was unpredictable in the short term, but displayed a predictable pattern in the long run. In Statistics, we are
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 informationChapter 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 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. Find a z-score satisfying the given condition. 1) 20.1% of the total area is to the right
More informationPCI VISA JCB 1.0 ! " #$&%'( I #J! KL M )+*, -F;< P 9 QR I STU. VXW JKX YZ\[X ^]_ - ` a 0. /\b 0 c d 1 * / `fe d g * /X 1 2 c 0 g d 1 0,
B! + BFḦ! + F s! ẗ ẅ ẍ!! þ! Š F!ñF+ + ±ŠFŌF ¹ F! FÀF +!±Š!+ÌÌ!!±! ±Š F!ñ±Š í îï!ñö øf!ù ûü ñń ¹F!!À!!! + B s s s s s B s s F ¹ ¹ ¹ ¹ Ì Ì ± ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ø ¹ ¹ ¹ ¹ ÀÀÀÀ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹
More informationDO NOT POST THESE ANSWERS ONLINE BFW Publishers 2014
Section 6.3 Check our Understanding, page 389: 1. Check the BINS: Binary? Success = get an ace. Failure = don t get an ace. Independent? Because you are replacing the card in the deck and shuffling each
More informationMAY 2005 EXAM FM SOA/CAS 2 SOLUTIONS
MAY 2005 EXAM FM SOA/CAS 2 SOLUTIONS Prepared by Sam Broverman http://wwwsambrovermancom 2brove@rogerscom sam@utstattorontoedu = 8l 8 " " 1 E 8 " œ@ = œ@ + œð" 3Ñ + œ + Á + (if 3Á! ) Ð" 3Ñ Answer: E 8l
More information2) There is a fixed number of observations n. 3) The n observations are all independent
Chapter 8 Binomial and Geometric Distributions The binomial setting consists of the following 4 characteristics: 1) Each observation falls into one of two categories success or failure 2) There is a fixed
More informationSTAT 3090 Test 2 - Version B Fall Student s Printed Name: PLEASE READ DIRECTIONS!!!!
STAT 3090 Test 2 - Fall 2015 Student s Printed Name: Instructor: XID: Section #: Read each question very carefully. You are permitted to use a calculator on all portions of this exam. You are NOT allowed
More informationTRUE-FALSE: Determine whether each of the following statements is true or false.
Chapter 6 Test Review Name TRUE-FALSE: Determine whether each of the following statements is true or false. 1) A random variable is continuous when the set of possible values includes an entire interval
More informationNovember 2001 Course 1 Mathematical Foundations of Actuarial Science. Society of Actuaries/Casualty Actuarial Society
November 00 Course Mathematical Foundations of Actuarial Science Society of Actuaries/Casualty Actuarial Society . An urn contains 0 balls: 4 red and 6 blue. A second urn contains 6 red balls and an unknown
More informationECEn 370 Introduction to Probability
RED- You can write on this exam. ECEn 7 Introduction to Probability Section Midterm Winter, Instructor Professor Brian Mazzeo Closed Book - You can bring one 8.5 X sheet of handwritten notes on both sides.
More informationExam 2 - Pretest DS-23
Exam 2 - Pretest DS-23 Chapter (4,5,6) Odds 10/3/2017 Ferbrache MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A single die
More informationChapter 8 Solutions Page 1 of 15 CHAPTER 8 EXERCISE SOLUTIONS
Chapter 8 Solutions Page of 5 8. a. Continuous. b. Discrete. c. Continuous. d. Discrete. e. Discrete. 8. a. Discrete. b. Continuous. c. Discrete. d. Discrete. CHAPTER 8 EXERCISE SOLUTIONS 8.3 a. 3/6 =
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 informationChapter 4 Probability Distributions
Slide 1 Chapter 4 Probability Distributions Slide 2 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions 4-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 4-5
More informationEXERCISES RANDOM VARIABLES ON THE COMPUTER
Exercises 383 RANDOM VARIABLES ON THE COMPUTER Statistics packages deal with data, not with random variables. Nevertheless, the calculations needed to find means and standard deviations of random variables
More informationChapter 2 and 3 Exam Prep Questions
1 You are given the following mortality table: q for males q for females 90 020 010 91 02 01 92 030 020 93 040 02 94 00 030 9 060 040 A life insurance company currently has 1000 males insured and 1000
More informationMATH 10 INTRODUCTORY STATISTICS
MATH 10 INTRODUCTORY STATISTICS Ramesh Yapalparvi Week 4 à Midterm Week 5 woohoo Chapter 9 Sampling Distributions ß today s lecture Sampling distributions of the mean and p. Difference between means. Central
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
AP Stats: Test Review - Chapters 16-17 Name Period MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the expected value of the random variable.
More information6.1 Discrete and Continuous Random Variables. 6.1A Discrete random Variables, Mean (Expected Value) of a Discrete Random Variable
6.1 Discrete and Continuous Random Variables 6.1A Discrete random Variables, Mean (Expected Value) of a Discrete Random Variable Random variable Takes numerical values that describe the outcomes of some
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 informationExercises for Chapter (5)
Exercises for Chapter (5) MULTILE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) 500 families were interviewed and the number of children per family was
More informationCHAPTER 6 Random Variables
CHAPTER 6 Random Variables 6.3 Binomial and Geometric Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Binomial and Geometric Random
More informationd) Find the standard deviation of the random variable X.
Q 1: The number of students using Math lab per day is found in the distribution below. x 6 8 10 12 14 P(x) 0.15 0.3 0.35 0.1 0.1 a) Find the mean for this probability distribution. b) Find the variance
More information2009 Plan Information Worksheet
Plan Sponsor Information 2009 Plan Information Worksheet Status: Plan Sponsor's Name Plan Sponsor's Mailling Address Foreign American University of Beirut 3 DAG Hammarskjold Plaza, 8th Floor Abbreviated
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Chapter 6 Exam A Name The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. 1) The probability of
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 informationEXCERPTS FROM S. BROVERMAN STUDY GUIDE FOR SOA EXAM FM/CAS EXAM 2 SPRING 2007
EXCERPTS FROM S. BROVERMAN STUDY GUIDE FOR SOA EXAM FM/CAS EXAM 2 SPRING 2007 Table of Contents Introductory Comments Section 12 - Bond Amortization, Callable Bonds Section 18 - Option Strategies (1) Problem
More informationSTUDY SET 1. Discrete Probability Distributions. x P(x) and x = 6.
STUDY SET 1 Discrete Probability Distributions 1. Consider the following probability distribution function. Compute the mean and standard deviation of. x 0 1 2 3 4 5 6 7 P(x) 0.05 0.16 0.19 0.24 0.18 0.11
More informationMETHODS AND ASSISTANCE PROGRAM 2014 REPORT Navarro Central Appraisal District. Glenn Hegar
METHODS AND ASSISTANCE PROGRAM 2014 REPORT Navarro Central Appraisal District Glenn Hegar Navarro Central Appraisal District Mandatory Requirements PASS/FAIL 1. Does the appraisal district have up-to-date
More informationRecord on a ScanTron, your choosen response for each question. You may write on this form. One page of notes and a calculator are allowed.
Ch 16, 17 Math 240 Exam 4 v1 Good SAMPLE No Book, Yes 1 Page Notes, Yes Calculator, 120 Minutes Dressler Record on a ScanTron, your choosen response for each question. You may write on this form. One page
More informationChapter 3. Discrete Probability Distributions
Chapter 3 Discrete Probability Distributions 1 Chapter 3 Overview Introduction 3-1 The Binomial Distribution 3-2 Other Types of Distributions 2 Chapter 3 Objectives Find the exact probability for X successes
More informationProbability & Statistics Chapter 5: Binomial Distribution
Probability & Statistics Chapter 5: Binomial Distribution Notes and Examples Binomial Distribution When a variable can be viewed as having only two outcomes, call them success and failure, it may be considered
More informationChapter 4 and Chapter 5 Test Review Worksheet
Name: Date: Hour: Chapter 4 and Chapter 5 Test Review Worksheet You must shade all provided graphs, you must round all z-scores to 2 places after the decimal, you must round all probabilities to at least
More informationProbability and Sample space
Probability and Sample space We call a phenomenon random if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions. The probability of any outcome
More informationKing Saud University Academic Year (G) College of Sciences Academic Year (H) Solutions of Homework 1 : Selected problems P exam
King Saud University Academic Year (G) 6 7 College of Sciences Academic Year (H) 437 438 Mathematics Department Bachelor AFM: M. Eddahbi Solutions of Homework : Selected problems P exam Problem : An auto
More informationMorningstar Rating Analysis
Morningstar Research January 2017 Morningstar Rating Analysis of European Investment Funds Authors: Nikolaj Holdt Mikkelsen, CFA, CIPM Ali Masarwah Content Morningstar European Rating Analysis of Investment
More informationImportant Terms. Summary. multinomial distribution 234 Poisson distribution 235. expected value 220 hypergeometric distribution 238
6 6 Summary Many variables have special probability distributions. This chapter presented several of the most common probability distributions, including the binomial distribution, the multinomial distribution,
More informationChapter 8: The Binomial and Geometric Distributions
Chapter 8: The Binomial and Geometric Distributions 8.1 Binomial Distributions 8.2 Geometric Distributions 1 Let me begin with an example My best friends from Kent School had three daughters. What is the
More information6. THE BINOMIAL DISTRIBUTION
6. THE BINOMIAL DISTRIBUTION Eg: For 1000 borrowers in the lowest risk category (FICO score between 800 and 850), what is the probability that at least 250 of them will default on their loan (thereby rendering
More informationl r,-i""r,:~-, Ross McEwan Gogarburn Edinburgh 13 July 2016 EH12 1 HQ
l r,-i""r,:~-, Ross McEan - I\\ -! ' ~ i'..,
More information