Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
8th Edition
ISBN: 9781259676512
Author: Kenneth H Rosen
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 7, Problem 6CP
enpositiveintegersjiandm,generatenirandompermutationsofthefirstiipositiveintegers. Sorteachpermutationusingtheversionofthebubble sortthatterrainateswhenapasshasbeenmadewthnointerchanges.countingtiienuinber of comparisons used, Determinetheaveragenumberof comparisons used over all mpermutatioDS.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Theaveragestartingsalaryforthisyear'sgraduatesatalargeuniversity(LU)is$20,000withastandarddeviationof$8,000.Furthermore,itisknownthatthestartingsalariesarenormallydistributed.a.WhatistheprobabilitythatarandomlyselectedLUgraduatewillhaveastartingsalaryofatleast$30,400?
b.WhatistheprobabilitythatarandomlyselectedLUgraduatewillhaveasalaryofexactly$30,400? &.Individualswithstartingsalariesoflessthan$15600receivealowincometaxbreak.Whatpercentageofthegraduateswillreceivethetaxbreak?
d.If189oftherecentgraduateshavesalariesofatleast$32240,howmanystudentsgraduatedthisyearfromthisuniversity?
Theaveragestartingsalaryforthisyear'sgraduatesatalargeuniversity(LU)is$20,000withastandarddeviationof$8,000.Furthermore,itisknownthatthestartingsalariesarenormallydistributed.
a.WhatistheprobabilitythatarandomlyselectedLUgraduatewillhaveastartingsalaryofatleast$30,400?
b.WhatistheprobabilitythatarandomlyselectedLUgraduatewillhaveasalaryofexactly$30,400?
c.Individualswithstartingsalariesoflessthan$15600receivealowincometaxbreak.
Whatpercentageofthegraduateswillreceivethetaxbreak?
d.If189oftherecentgraduateshavesalariesofatleast$32240,howmanystudentsgraduatedthisyearfromthisuniversity?
The director of the MBA program at Salterdine University wants to develop a procedure to determine which applicants to admit to the MBA program. The director believes that an applicant’s undergraduate grade point average (GPA) and score on the GMAT exam are helpful in predicting which applicants will be good students. To assist in this endeavor, the director asked a committee of faculty members to classify 70 of the recent students in the MBA program into two groups: (1) good students and (2) weak students. The file MBAStudents.xlsm summarizes these ratings, along with the GPA and GMAT scores for the 70 students.
What are the coordinates of the centroids for the good students and the weak students?
Use XLMiner’s standard data partition command to partition the data into a training set (with 60% of the observations) and validation set (with 40% of the observations) using the default seed of 12345.
Use discriminant analysis to create a classifier for this data. How accurate is this…
Chapter 7 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Ch. 7.1 - i. What is the probability that a card selected at...Ch. 7.1 - t istheprobability that a fair die comes up six...Ch. 7.1 - t is the probability that a randomly selected...Ch. 7.1 - What is the probability7that a randomly selected...Ch. 7.1 - t is the probability that the sum of the numbers...Ch. 7.1 - t is the probability that a card selected at...Ch. 7.1 - t is the probability that when a coin is flipped...Ch. 7.1 - t is the probability that a five-card poker hand...Ch. 7.1 - t is the probability that a five-card poker hand...Ch. 7.1 - t is the probability that a five-card poker hand...
Ch. 7.1 - Prob. 11ECh. 7.1 - t is the probability that afive-card poker hand...Ch. 7.1 - t is the probability tliat afive-card poker hand...Ch. 7.1 - t istheprobability that a five-card poker hand...Ch. 7.1 - t is theprobabilifrthatafive-cardpoker hand...Ch. 7.1 - t is the probability7that a five-card poker hand...Ch. 7.1 - Prob. 17ECh. 7.1 - Mat is the probability' that a five-card poker...Ch. 7.1 - Prob. 19ECh. 7.1 - probabihh’thatafiM^Ch. 7.1 - Prob. 21ECh. 7.1 - t is the probability that a positive integer not...Ch. 7.1 - t is the probability that a positive integer not...Ch. 7.1 - Prob. 24ECh. 7.1 - - Find the probability of winning a lottery by...Ch. 7.1 - 26.Find the pr obabilitj- of selecting none of the...Ch. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - i$theprobabilitytiiatAbby,Barry,andSy^...Ch. 7.1 - 34.Mat is the probability' that Bo, Colleen, Jeff,...Ch. 7.1 - roulette, a wheel with 38 numbers is spun. Of...Ch. 7.1 - ch is more likely: rolling a total of 8 when two...Ch. 7.1 - ch is more likely: rolling a total of 9 when hvo...Ch. 7.1 - A player in the Mega Millions lottery picks five...Ch. 7.1 - a player buys a Mega Millions ticket in many...Ch. 7.1 - A player in the Powerball lottery picks five...Ch. 7.1 - Aplayer in the Powerball lottery (see Exercise 40)...Ch. 7.1 - Two events E i and E2are calledindependentifp(Etfl...Ch. 7.1 - Prob. 43ECh. 7.1 - Suppose that instead of three doors, there are...Ch. 7.1 - s problem was posed by the Chevalier de Mere and...Ch. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - w that conditions (2) and (22) are met under...Ch. 7.2 - A pair of dice is loaded. The probability that a 4...Ch. 7.2 - t is the probability of these events when we...Ch. 7.2 - t is the probability of these events when we...Ch. 7.2 - 8.What is the probability of these events when we...Ch. 7.2 - t is the probability of these events when we...Ch. 7.2 - What is the probability of these events when we...Ch. 7.2 - pose, that £ and F are. events such that d(£)=0.7...Ch. 7.2 - pose that £ and Fare events such thatp(£) = 0.8...Ch. 7.2 - w that if £ and F are events, thenpfEn F) >p(E) +...Ch. 7.2 - Use mathematical induction to prove the following...Ch. 7.2 - w that if £x, £2,Enare events from afinite sample...Ch. 7.2 - Show that iff and f are independent events,...Ch. 7.2 - 17,It £ and F are independent events, prove or...Ch. 7.2 - What is the probability that hvo people chosen at...Ch. 7.2 - Mat is the probability that two people chosen at...Ch. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - February 29 occurs only inleap years, Years...Ch. 7.2 - ^Tiat is the conditional probabilitv that exactly...Ch. 7.2 - What is the. conditional probabilih' that exactly...Ch. 7.2 - Prob. 25ECh. 7.2 - Let Ebe the event that aranmly generated bit...Ch. 7.2 - Prob. 27ECh. 7.2 - a8. Assume that the probability a child is a boy...Ch. 7.2 - A group of six people play the game of “ odd...Ch. 7.2 - Find the probability that a randomly generated bit...Ch. 7.2 - Find the probability that a family with five...Ch. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Find each of the following probabilities...Ch. 7.2 - d each of the following probabilities...Ch. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - 38.A pair of dice is rolled in a remote location...Ch. 7.2 - This exercise employs the probabilistic method to...Ch. 7.2 - Dense a Monte Carlo algorithm that determines...Ch. 7.2 - pseudocode to write out the probabilistic...Ch. 7.3 - i.Suppose that £ andFare events in a sample space...Ch. 7.3 - Suppose that Land Fare events in a sample space...Ch. 7.3 - 3.Suppose that Frida selects a ball by first...Ch. 7.3 - 4.Suppo s e that Ann selects a ball by first...Ch. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - 8,Suppose that one person in 10,000 people has a...Ch. 7.3 - Suppose that 8% of the patients tested in a clinic...Ch. 7.3 - io,Suppose that 4% of the patients tested in a...Ch. 7.3 - ...Ch. 7.3 - ...Ch. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - In this exercise we will use Bayes' theorem to...Ch. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - 18.Suppose that a Bayesian spam filter is trained...Ch. 7.3 - 19,Suppose that a Bayesian spam filter is trained...Ch. 7.3 - Prob. 20ECh. 7.3 - ,Suppose that a Bayesian spam filter is trained on...Ch. 7.3 - Suppose that we have prior information concerning...Ch. 7.3 - Prob. 23ECh. 7.4 - t is the expected number of heads that come up...Ch. 7.4 - t is the expected number of heads that come up...Ch. 7.4 - t is the expected number of times a 6 appears when...Ch. 7.4 - A coin is biased so that the probability a head...Ch. 7.4 - ^Tiat is the expected sum of the numbers that...Ch. 7.4 - Prob. 6ECh. 7.4 - final exam of a discrete mathematics course...Ch. 7.4 - t is the expected sum of the numbers that appear...Ch. 7.4 - Prob. 9ECh. 7.4 - Suppose that we flip a fair coin until either it...Ch. 7.4 - Suppose that we roll a fair die until a 6 conies...Ch. 7.4 - pose that we roll a fair die until a 6 comes up....Ch. 7.4 - pose thatwerollapairoffair dice...Ch. 7.4 - Show that the sum of the probabilities of a random...Ch. 7.4 - Show that if the random variable A'has the...Ch. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Show that if J2,...,Xnare mutually independent...Ch. 7.4 - What is the expected value of the sum of the...Ch. 7.4 - as.Provethelaw of total expectations.Ch. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - A run is a maximal sequence of successes in a...Ch. 7.4 - a6.Let J(s) be a random variable, where I(s) is a...Ch. 7.4 - What is the variance of the number of heads that...Ch. 7.4 - t is the variance ot the number of times a 6...Ch. 7.4 - LetXnbe the random variable that equals the number...Ch. 7.4 - w that ifXand Fare independent random variables,...Ch. 7.4 - Prob. 31ECh. 7.4 - Pronde an example that shows that the variance of...Ch. 7.4 - pose that A\ andX2are independent Bernoulli trials...Ch. 7.4 - Prove the general caseofTheoremy. That is, show...Ch. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - pose that the number of cans of soda pop filled in...Ch. 7.4 - 39.Suppose that the number of aluminum cans...Ch. 7.4 - pose the probabilitvthatxis the...Ch. 7.4 - In this exercise we derive an estimate of the...Ch. 7.4 - Prob. 42ECh. 7.4 - to is the variance of the number of fixed...Ch. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7 - Define the probability of an event when all...Ch. 7 - WTiat conditions should be met by the...Ch. 7 - Define, the conditional probability’ of an event £...Ch. 7 - Prob. 4RQCh. 7 - tois a random variable? toare the possible values...Ch. 7 - Prob. 6RQCh. 7 - Explain how the average-case computational...Ch. 7 - Prob. 8RQCh. 7 - What does the linearity of expectations of random...Ch. 7 - Prob. 10RQCh. 7 - Prob. 11RQCh. 7 - Prob. 12RQCh. 7 - Prob. 13RQCh. 7 - What is the variance of the sum of n independent...Ch. 7 - Prob. 15RQCh. 7 - Prob. 1SECh. 7 - 2012, a player in the Mega Millions lottery picks...Ch. 7 - 2012, a player in the Powerball lottery picks five...Ch. 7 - t is the probability that a hand of 13 cards...Ch. 7 - t is the probability that a 13-card bridge hand...Ch. 7 - t is the probability that a seven-card poker hand...Ch. 7 - What is the expected value of the number that...Ch. 7 - What is the expected value of the number that...Ch. 7 - Suppose that a pair of fair octahedral dice is...Ch. 7 - io.Suppose that a pair offaiir dodecahedral diceis...Ch. 7 - ii.Supp o s e that a fair standard (cubic) die and...Ch. 7 - Prob. 12SECh. 7 - (mpeople!n>3!play“oddp™ut’todeadeMo^...Ch. 7 - Prob. 14SECh. 7 - posethatmandnarepositiYeintegers.Bat is...Ch. 7 - pose thatEt, E2,Enarenevents with p(£j) >o fori...Ch. 7 - Prob. 17SECh. 7 - t is the probability that when a fair coin is...Ch. 7 - t is the probability that a randomly selected bit...Ch. 7 - t is the probability that a randomly selected bit...Ch. 7 - sider the following game. A per son flips a coin...Ch. 7 - pose that n halls are tossed intobbins so that...Ch. 7 - posethatAandBareeventswthprobabilitiesp(A) =...Ch. 7 - posethat/l andB are events...Ch. 7 - all fromDefinition jinSection 7,2that the events...Ch. 7 - ...Ch. 7 - Prob. 27SECh. 7 - Prob. 28SECh. 7 - Prob. 29SECh. 7 - Prob. 30SECh. 7 - Prob. 31SECh. 7 - Prob. 32SECh. 7 - Prob. 33SECh. 7 - maximum satisfiability problemasks for an...Ch. 7 - Prob. 35SECh. 7 - The following method can be used to generate a...Ch. 7 - Prob. 1CPCh. 7 - Prob. 2CPCh. 7 - Prob. 3CPCh. 7 - Prob. 4CPCh. 7 - Prob. 5CPCh. 7 - ...Ch. 7 - Prob. 7CPCh. 7 - Prob. 8CPCh. 7 - Prob. 9CPCh. 7 - ulaterepeated trials oftheMoufr Hall Three-Door...Ch. 7 - Prob. 11CPCh. 7 - Prob. 1CAECh. 7 - Prob. 2CAECh. 7 - Prob. 3CAECh. 7 - Prob. 4CAECh. 7 - Prob. 5CAECh. 7 - Prob. 6CAECh. 7 - Prob. 7CAECh. 7 - Prob. 8CAECh. 7 - cribe the origins of probability theory and the...Ch. 7 - Prob. 2WPCh. 7 - 3.Discuss the probability' of winning when you...Ch. 7 - estigate the game of craps and discuss the...Ch. 7 - Prob. 5WPCh. 7 - Prob. 6WPCh. 7 - lain how Erdos and Renvi first used the...Ch. 7 - cuss the different types of probabilistic...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- The following table below shows the number of employees in the four divisions of a corporation. There are 85 new computers that are to be apportioned among the divisions based on the number of employees in each division. a. Use the Hamilton method to determine the number of computers to be apportioned to each division. b. Use the Jefferson method to determine the number of computers to be apportioned to each division. Does this particular apportionment violate the quota rule? c. Suppose the supplier of the computers decided to reward the corporation with one unit of computer and delivered it just after the deployment of the 85 units. Use the Huntington-Hill apportionment principle to determine which division will get one additional unit?arrow_forwardA Not for profit Organization (NPO) wants to create a sample of financially backward girl students who are unable to continue their higher education, from the AL Dakhliya governorate. The organization wishes to sponsor the students’ higher education expenses. For this purpose in the first stage, the NGO randomly selects some wilayats from the 8 wilayats in the Al Dakhliya governorate to form a sample and then selects all girl students from the selected wilayats to extend help to them by providing sponsorship for their higher education. Which among the following statement is true about the sampling method chosen here? a. This method is based on the judgement of the researcher b. It is a probability sampling method c. It is a non- probability sampling method d. This method is also known as judgement samplingarrow_forwardA Not for profit Organization (NPO) wants to create a sample of financially backward girl students who are unable to continue their higher education, from the AL Dakhliya governorate. The organization wishes to sponsor the students’ higher education expenses. For this purpose in the first stage, the NGO randomly selects some wilayats from the 8 wilayats in the Al Dakhliya governorate to form a sample and then selects all girl students from the selected wilayats to extend help to them by providing sponsorship for their higher education. What is the method of sampling used here? a. Convenience Sampling b. Systematic sampling c. Stratified sampling d. Cluster Samplingarrow_forward
- According to the Mines and Geosciences Bureau (MGB) Region 6 identified the top 2 districts with the most number of barangays prone to flooding. Moreover, they have also whether these barangays are "very nigh of "high" susceptibility to flooding. In Jaro, nine barangays have "very high" flooding risk. These'are San Isidro, (5) Sambag, (6) Ungka, (7) Lanit, (8) Buntatala, and (9) Tagbak. identified (yCalubihan, (2) Buhang, (3) Dungon-A, (4) The Jaro barangays with 18 "high" flooding risk are (1) Montinola, (2) Taytay Zone 2, (3) Desamparados, (4) Cuartero, (5) Ma. Christina, (6) San Roque, (7) Simon Ledesma, (8) Democracia, (9) Tabuc Suba, (10) Cubay, (11) Balabago, (12) MV Hechanova, (13) Quintin Salas, (14) Tacas, (15) Dungon B., (16) Camalig, (17): Arguelles, and (18) El 98. In Mandurriao, four villages with "very high" susceptibility to flooding are (1) Tabucan, (2) Bakhaw, (3) Buhang Taft North, and (4) Santa Rosa. Barangays deemed with "high" flood exposure risk are (1) San…arrow_forwardAccording to the Department of Motor Vehicles (DMV), the entity in charge ofprovidingdrivinglicensesintheUnitedStates,itisillegaltodrivewithabloodalcoholcontentof0.08%ormoreif you are 21 or older. In the DMV’s guidelines to determine when a person is driving under the influence, itisindicatedthatfewer than five percent of the population weighing 100 pounds will exceed the 0.33 alcohol level. Assume this is accurate. If the Highway Patrol stops in a random day 200 unrelated cars where the individual weighs one hundred pounds, on a Friday night, what is the probability that six percent of more individuals stopped exceeds that 0.33 alcohol level?arrow_forwardOn a 10-member board, Company A (with 850 stockholders) has 3 representatives while Company B(with 1,200 stockholders) has 4 representatives. Calculate the relative unfairness of this apportionment.arrow_forward
- wat is the intermdiate demond of the agricultural,manufacutring,and energy sectorarrow_forwardTroye teaches two undergraduate Accounting courses at UST. The class for Income Taxationconsists of 6 sophomores and 4 juniors. The more advanced course, Business Taxation, has 7sophomores and 2 juniors. As an example of a business sampling technique, Professor Shanerandomly selects, from the stack of Income Taxation registration cards, the class card of onestudent and then replaces the card in the stack. If that student was a sophomore, Shane drawsanother card from the Income Taxation stack; if not, she randomly draws a card from the BusinessTaxation group. What is the probability of: Interpret your answers. a. A junior’s name on both draws?b. A junior’s name on the first draw?c. A sophomore’s name on both draws?d. A junior’s name on the second draw, given that a sophomore’s name was drawn on first? 2. P(ace or jack)?3. P(club or non-club)?4. P(club or black)?5. P(heart or red card)?6. P(club or spade)?arrow_forwardIf a set of exam scores forms a positively skewed distributition, it suggest that the majortiy of students did not score well on the exam. True or False?arrow_forward
- there are 120 teachers.select a sample of 40 teachers by using the systematic technique.arrow_forwardThe director of a local shopping mall draws a name out of a box of entries to determine who will win a $100,000 shopping spree. O random systematic convenience O stratified clusterarrow_forward1. The College of Science surveys its graduating students to determine the starting salaries and the job market for the new graduates. The population of graduating students according to major is recorded as follows: BS Bio (85), BSM- CS (102), BSM- BA (78), and BSM- AS (75). If you would like to select 100 samples, how large must a sample be for each major using proportionate allocation? 2. The event organizer plans to give 9 complimentary tickets to the presidents of the school organizations so they can attend the upcoming event for free. Since the tickets will be given only to 9 out of 50 presidents, the event organizer decided to choose a systematic random sampling procedure. Determine k (sampling interval). Let the random start be at number three (3). List the number of the first three samples.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY