Finite Mathematics & Its Applications (12th Edition)
12th Edition
ISBN: 9780134437767
Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
Publisher: PEARSON
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Textbook Question
Chapter 5.5, Problem 59E
Seating Arrangements In the quiz show It’s Academic, three person teams from three high schools are seated in a row, with each team seated together. How many different seating arrangements are possible?
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Total marks 16
5.
Let (N,F,P) be a probability space and let X : N → R be a
random variable such that the probability density function is given by
f(x)=ex for x € R.
(i)
Find the characteristic function of the random variable X.
[8 Marks]
(ii) Using the result of (i), calculate the first two moments of
the random variable X, i.e., E(X") for n = 1,2.
(iii)
What is the variance of X.
[6 Marks]
[2 Marks]
Chapter 5 Solutions
Finite Mathematics & Its Applications (12th Edition)
Ch. 5.1 - Solutions can be found following the section...Ch. 5.1 - Solutions can be found following the section...Ch. 5.1 - Solutions can be found following the section...Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7E
Ch. 5.1 - 8. Corporations Let {all corporations}, all...Ch. 5.1 - SP Index The Standard and Poors Index measures the...Ch. 5.1 - 10. S&P Index Refer to Table 3 on the next page....Ch. 5.1 - SP Index Refer to Exercise 9. Describe in words...Ch. 5.1 -
12. S&P Index Refer to Exercise 10. Describe in...Ch. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - In Exercises 15–20, simplify each given...Ch. 5.1 - In Exercises 1520, simplify each given expression....Ch. 5.1 - In Exercises 1520, simplify each given expression....Ch. 5.1 - Prob. 18ECh. 5.1 - In Exercises 15–20, simplify each given...Ch. 5.1 - Prob. 20ECh. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - College Teachers and Students Let U= {people at...Ch. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - College Teachers and Students Let {people at Mount...Ch. 5.1 - College Teachers and Students Let {people at Mount...Ch. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - 47. Let U be the set of vertices in Fig. 1. Let, ...Ch. 5.1 - 48. Let U be the set of vertices in Fig. 1. Let, ...Ch. 5.1 - Sandwich Toppings Eds Cheesesteaks offers any...Ch. 5.1 - Toppings Choices Amy ordered a baked potato at a...Ch. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Find three subsets of the set of integers from 1...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.1 - In Exercises 5562, determine whether the statement...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.1 - In Exercises 5562, determine whether the statement...Ch. 5.1 - In Exercises 5562, determine whether the statement...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.2 - Prob. 1CYUCh. 5.2 - Prob. 2CYUCh. 5.2 - 1. Find , given that , and .
Ch. 5.2 - Find n(ST), given that n(S)=17,n(T)=13, and...Ch. 5.2 - 3. Find , given that , and .
Ch. 5.2 - Find n(ST), given that n(S)=4,n(T)=12, and...Ch. 5.2 - 5. Find , given that , and .
Ch. 5.2 - 6. Find , given that , and .
Ch. 5.2 - If n(S)=n(ST), what can you conclude about S and...Ch. 5.2 - If n(T)=n(ST), what can you conclude about S and...Ch. 5.2 - 9. Languages Suppose that each of the 314 million...Ch. 5.2 - 10. Course Enrollments Suppose that all of the...Ch. 5.2 - 11. Symmetry of Letters Of the 26 capital letters...Ch. 5.2 - 12. Streaming Subscriptions A survey of employees...Ch. 5.2 - Automobile Options Motors Inc. manufactured 325...Ch. 5.2 - 14. Investments A survey of 120 investors in...Ch. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - In Exercises 39–44, use De Morgan’s laws to...Ch. 5.2 - In Exercises 3944, use De Morgans laws to simplify...Ch. 5.2 - In Exercises 39–44, use De Morgan’s laws to...Ch. 5.2 - In Exercises 3944, use De Morgans laws to simplify...Ch. 5.2 - Prob. 43ECh. 5.2 - In Exercises 39–44, use De Morgan’s laws to...Ch. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - By drawing a Venn diagram, simplify each of the...Ch. 5.2 - Prob. 52ECh. 5.2 - By drawing a Venn diagram, simplify each of the...Ch. 5.2 - Prob. 54ECh. 5.2 - Citizenship Assume that the universal set U is the...Ch. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Citizenship Assume that the universal set U is the...Ch. 5.3 - Of the 1000 first-year students at a certain...Ch. 5.3 - 2. Refer to the Venn diagram from Problem...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Music Preferences A survey of 70 high school...Ch. 5.3 - 24. Nobel Winners A total of 900 Nobel Prizes had...Ch. 5.3 - 25. Analysis of Sonnet One of Shakespeare’s...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Class Enrollment Out of 35 students in a finite...Ch. 5.3 - Exercise Preferences A survey of 100 college...Ch. 5.3 - Exercises 33–38 refer to the 193 flags.
33. How...Ch. 5.3 - Exercises 3338 refer to the 193 flags. How many...Ch. 5.3 - Exercises 3338 refer to the 193 flags. How many...Ch. 5.3 - Exercises 33–38 refer to the 193 flags.
36. How...Ch. 5.3 - Exercises 33–38 refer to the 193 flags.
37. How...Ch. 5.3 - Exercises 3338 refer to the 193 flags. How many...Ch. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Course Enrollments Table 1 shows the number of...Ch. 5.3 - Prob. 46ECh. 5.3 - Use a Venn diagram to find the number of people in...Ch. 5.3 - Use a Venn diagram to find the number of people in...Ch. 5.3 - Prob. 49ECh. 5.3 - Use a Venn diagram to find the number of people in...Ch. 5.3 - 51. Voting Preferences One hundred college...Ch. 5.3 - Union Membership and Education Status A group of...Ch. 5.3 - Diagnostic Test Results A class of 30 students was...Ch. 5.3 - Air-Traffic Controllers A group of applicants for...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Website Preferences One hundred and sixty business...Ch. 5.3 - Small Businesses A survey of the characteristics...Ch. 5.3 - 71. Music Each of the 100 students attending a...Ch. 5.3 - Prob. 72ECh. 5.4 - There are five seats available in a sedan. In how...Ch. 5.4 - 2. A multiple-choice exam contains 10 questions,...Ch. 5.4 - 1. Jolene wants to drive from her house to the...Ch. 5.4 - 2. There are three bridges from the west shore of...Ch. 5.4 - Travel Options If you can travel from Frederick,...Ch. 5.4 - Travel Options Suppose that Maria wants to go from...Ch. 5.4 - Daytona 500 Forty-four race cars competed in the...Ch. 5.4 - Kentucky Derby Twenty horses competed in the 2016...Ch. 5.4 - 7. Winners Twenty athletes enter an Olympic event....Ch. 5.4 - 8. Ranking Teams A sportswriter is asked to rank...Ch. 5.4 - 9. Electing Captains A football squad can elect a...Ch. 5.4 - Club Officers A club can elect a president and a...Ch. 5.4 - 11. Group Picture A group of five boys and three...Ch. 5.4 - Arranging Books Three history books and six novels...Ch. 5.4 - 13. Rearranging Letters How many different words...Ch. 5.4 - Three-Letter Words How many different three-letter...Ch. 5.4 - 15. Selecting an Outfit How many different outfits...Ch. 5.4 - Selecting an Outfit How many different outfits can...Ch. 5.4 - Serial Numbers A computer manufacturer assigns...Ch. 5.4 - 18. License Plates Suppose that a license plate...Ch. 5.4 - Social Security Numbers How many Social Security...Ch. 5.4 - 20. Call Letters In 1923, the Federal...Ch. 5.4 - 21. Area Codes Before 1995, three-digit area codes...Ch. 5.4 - 22. Area Codes Refer to Exercise 21. Beginning in...Ch. 5.4 - Palindromes A number or word is said to be a...Ch. 5.4 - Palindromes A number or word is said to be a...Ch. 5.4 - Palindromes A number or word is said to be a...Ch. 5.4 - 26. How many 3-letter words (including nonsense...Ch. 5.4 - 27. World Series The World Series of Baseball is...Ch. 5.4 - 28. Super Bowl The Super Bowl is a game played...Ch. 5.4 - 29. Bridge Games There are 3200 duplicate bridge...Ch. 5.4 - Ice Cream Selections An ice cream parlor offers 25...Ch. 5.4 - Internet Accounts A college of 20,000 students...Ch. 5.4 - 32. Pairs of Initials A company has 700 employees....Ch. 5.4 - 33. Game Outcomes The final score in a soccer game...Ch. 5.4 - Selecting an Outfit Each day, Gloria dresses in a...Ch. 5.4 - Mismatched Gloves A man has five different pairs...Ch. 5.4 - 36. Mismatched Shoes Fred has 11 different pairs...Ch. 5.4 - Coin Tosses Toss a coin six times, and observe the...Ch. 5.4 - 38. Coin Tosses Refer to Exercise 37. In how many...Ch. 5.4 - 39. Exam Questions An exam contains five...Ch. 5.4 - Exam Questions An exam contains five true-or-false...Ch. 5.4 - 41. Exam Questions Each of the 10 questions on a...Ch. 5.4 - 42. Exam Questions Rework Exercise 41 under the...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - Shading of Venn Diagrams How many different ways...Ch. 5.4 - Shading of Venn Diagrams How many different ways...Ch. 5.4 - Roulette An American roulette wheel consists of 38...Ch. 5.4 - Roulette An American roulette wheel consists of 38...Ch. 5.4 - Batting Orders The manager of a Little League...Ch. 5.4 - Test Volunteers A physiologist wants to test the...Ch. 5.4 - Handshakes Two 10-member basketball teams play a...Ch. 5.4 - 58. Band Selections In how many ways can a band...Ch. 5.4 - 59. Colored Houses Six houses in a row are each to...Ch. 5.4 - Chair Varieties A furniture manufacturer makes...Ch. 5.4 - 61. Ballots Seven candidates for mayor, four...Ch. 5.4 - College Applications Allison is preparing her...Ch. 5.4 - Paths to Texas Consider the triangular display of...Ch. 5.4 - Prob. 64ECh. 5.5 - Calculate the following values: (a) 5! (b) P(5,5)...Ch. 5.5 - 2. A newborn child is to be given a first name and...Ch. 5.5 - For Exercises 1–20, calculate the values.
1.
Ch. 5.5 - For Exercises 120, calculate the values. P(5,1)Ch. 5.5 - For Exercises 1–20, calculate the values.
3.
Ch. 5.5 - For Exercises 120, calculate the values. P(5,4)Ch. 5.5 - For Exercises 120, calculate the values. C(10,3)Ch. 5.5 - For Exercises 1–20, calculate the values.
6.
Ch. 5.5 - For Exercises 120, calculate the values. C(5,4)Ch. 5.5 - For Exercises 120, calculate the values. C(6,3)Ch. 5.5 - For Exercises 120, calculate the values. P(7,1)Ch. 5.5 - For Exercises 1–20, calculate the values.
10.
Ch. 5.5 - For Exercises 120, calculate the values. P(n,1)Ch. 5.5 - For Exercises 120, calculate the values. P(n,2)Ch. 5.5 - For Exercises 120, calculate the values. C(4,4)Ch. 5.5 - For Exercises 120, calculate the values. C(n,2)Ch. 5.5 - For Exercises 1–20, calculate the values.
15.
Ch. 5.5 - For Exercises 120, calculate the values. C(n,1)Ch. 5.5 - For Exercises 1–20, calculate the values.
17.
Ch. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - For Exercises 120, calculate the values. 7!Ch. 5.5 - In Exercises 2126, determine whether the...Ch. 5.5 - In Exercises 2126, determine whether the...Ch. 5.5 - In Exercises 21–26, determine whether the...Ch. 5.5 - In Exercises 21–26, determine whether the...Ch. 5.5 - In Exercises 21–26, determine whether the...Ch. 5.5 - In Exercises 2126, determine whether the...Ch. 5.5 - 27. Group Picture In how many ways can four people...Ch. 5.5 - 28. Waiting in Line In how many ways can six...Ch. 5.5 - Book Selection How many different selections of...Ch. 5.5 - Pizza Varieties A pizzeria offers five toppings...Ch. 5.5 - Selecting Colleges A high school student decides...Ch. 5.5 - Senate Committees In how many different ways can a...Ch. 5.5 - 33. Ranking Teams A sportswriter makes a preseason...Ch. 5.5 - 34. CD Changer Suppose that you have 36 CDs and...Ch. 5.5 - Guest Lists How many ways can you choose five out...Ch. 5.5 - Choosing Exam Questions A student is required to...Ch. 5.5 - 37. DVDs In a batch of 100 DVDs, seven are...Ch. 5.5 - Debates There are 17 candidates for an elected...Ch. 5.5 - 39. Race Winners Theoretically, assuming no ties,...Ch. 5.5 - 40. Player Introductions The five starting players...Ch. 5.5 - Poker Hands Exercises 41–44 refer to poker hands....Ch. 5.5 - Poker Hands Exercises 4144 refer to poker hands. A...Ch. 5.5 - Poker Hands Exercises 41–44 refer to poker hands....Ch. 5.5 - Poker Hands Exercises 4144 refer to poker hands. A...Ch. 5.5 - 45. Distributing Sandwiches Five students order...Ch. 5.5 - 46. Nautical Signals A nautical signal consists of...Ch. 5.5 - 47. Selecting Sweaters Suppose that you own 10...Ch. 5.5 - Distributing Books Fred has 12 different books....Ch. 5.5 - Conference Games In an eight-team football...Ch. 5.5 - 50. League Games In a six-team softball league,...Ch. 5.5 - Powerball In the Powerball lottery, five white...Ch. 5.5 - Baseball Lineup On a childrens baseball team,...Ch. 5.5 - Lotto Exercises 53 and 54 refer to the New York...Ch. 5.5 - Lotto Exercises 53 and 54 refer to the New York...Ch. 5.5 - Choosing Candy Two children, Moe and Joe, are...Ch. 5.5 - Committee Selection The 12 members of the Gotham...Ch. 5.5 - Group Picture The student council at Gotham...Ch. 5.5 - Arranging Books George has three books by each of...Ch. 5.5 - Seating Arrangements In the quiz show Its...Ch. 5.5 - Displaying Paintings An art gallery has four...Ch. 5.5 - 61. Handshakes At a party, everyone shakes hands...Ch. 5.5 - 62. Football Games In a football league, each team...Ch. 5.5 - 63. Side Dishes A restaurant offers its customers...Ch. 5.5 - Ice Cream Specials An ice cream parlor offers a...Ch. 5.5 - 65. Determine Position There are six-letter words...Ch. 5.5 - Detour-Prone ZIP Codes A five-digit ZIP code is...Ch. 5.5 - 67. Lottery
(a) Calculate the number of possible...Ch. 5.5 - Bridge A bridge hand contains 13 cards. (a) What...Ch. 5.5 - 69. Cards versus Atoms Are there more ways to...Ch. 5.5 - Alphabet versus Atoms Are there more ways to...Ch. 5.6 - School Board A newspaper reporter wants an...Ch. 5.6 - 2. Free Throws A basketball player shoots eight...Ch. 5.6 - 1. Tossing a Coin An experiment consists of...Ch. 5.6 - 2. Tossing a Coin An experiment consists of...Ch. 5.6 - 3. Tossing a Coin An experiment consists of...Ch. 5.6 - 4. Tossing a Coin An experiment consists of...Ch. 5.6 - 5. World Series In the World Series, the American...Ch. 5.6 - World Series Refer to Exercise 5. How many...Ch. 5.6 - Game Outcomes A football team plays 11 games. In...Ch. 5.6 - 8. Game Outcomes A chess master plays 15 games. In...Ch. 5.6 - Bytes Exercises 9 and 10 refer to computer bytes....Ch. 5.6 - Bytes Exercises 9 and 10 refer to computer bytes....Ch. 5.6 - 11. Routes through City Streets Refer to the map...Ch. 5.6 - Routes through City Streets Refer to the map in...Ch. 5.6 - Routes through City Streets Refer to the map in...Ch. 5.6 - Routes through City Streets Refer to the map in...Ch. 5.6 - 15. Routes through City Streets Refer to the map...Ch. 5.6 - 16. Routes through City Streets Refer to the map...Ch. 5.6 - 17. Routes through City Streets Refer to the map...Ch. 5.6 - Routes through City Streets Imagine a street map...Ch. 5.6 - Tossing a Coin A coin is tossed 10 times, and the...Ch. 5.6 - 20. Arranging Books Four mathematics books and...Ch. 5.6 - 21. Seating Arrangements In how many ways can six...Ch. 5.6 - Photo Session In 2015, there were three women and...Ch. 5.6 - 23. Selecting Balls from an Urn An urn contains 12...Ch. 5.6 - 24. Selecting Balls from an Urn An urn contains 15...Ch. 5.6 - Selecting Apples A bag of 10 apples contains 2...Ch. 5.6 - Selecting Light Bulbs A package contains 100 LED...Ch. 5.6 - Subcommittee Selection A committee has four male...Ch. 5.6 - 28. Investment Portfolio In how many ways can an...Ch. 5.6 - Poker Hands Exercises 29–32 refer to poker hands....Ch. 5.6 - Poker Hands Exercises 2932 refer to poker hands. A...Ch. 5.6 - Poker Hands Exercises 2932 refer to poker hands. A...Ch. 5.6 - Poker Hands Exercises 2932 refer to poker hands. A...Ch. 5.6 - In Exercises 33–36, a “word” is interpreted to be...Ch. 5.6 - In Exercises 33–36, a “word” is interpreted to be...Ch. 5.6 - In Exercises 3336, a word is interpreted to be a...Ch. 5.6 - In Exercises 33–36, a “word” is interpreted to be...Ch. 5.6 - Photo Session In 2015, there were three women and...Ch. 5.6 - 38. Seating Arrangements You, a friend, and four...Ch. 5.6 - Numbers In how many five-digit numbers (without...Ch. 5.6 - Alphabetical Order In how many four-letter words...Ch. 5.6 - License Plates Suppose that license plates from a...Ch. 5.6 - 42. License Plates Suppose that license plates...Ch. 5.6 - Seating Arrangements A family has 12 members. In...Ch. 5.6 - Prob. 44ECh. 5.6 - Prob. 45ECh. 5.6 - Tossing a Coin What percent of the possible...Ch. 5.6 - Prob. 47ECh. 5.6 - 48. Selecting Balls from an Urn Suppose that a...Ch. 5.7 - Calculate (128).Ch. 5.7 - 2. An ice cream parlor offers 10 flavors of ice...Ch. 5.7 - Prob. 1ECh. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Prob. 5ECh. 5.7 - Calculate the value for each of Exercises...Ch. 5.7 - Calculate the value for each of Exercises...Ch. 5.7 - Calculate the value for each of Exercises 1-18....Ch. 5.7 - Prob. 9ECh. 5.7 - Calculate the value for each of Exercises 1-18....Ch. 5.7 - Prob. 11ECh. 5.7 - Prob. 12ECh. 5.7 - Prob. 13ECh. 5.7 - Prob. 14ECh. 5.7 - Prob. 15ECh. 5.7 - Calculate the value for each of Exercises 1-18....Ch. 5.7 - Calculate the value for each of Exercises...Ch. 5.7 - Calculate the value for each of Exercises 1-18....Ch. 5.7 - Prob. 19ECh. 5.7 - How many terms are there in the binomial expansion...Ch. 5.7 - 21. Determine the first three terms in the...Ch. 5.7 - 22. Determine the first three terms in the...Ch. 5.7 - 23. Determine the last three terms in the binomial...Ch. 5.7 - Determine the last three terms in the binomial...Ch. 5.7 - Determine the middle term in the binomial...Ch. 5.7 - 26. Determine the middle term in the binomial...Ch. 5.7 - Determine the coefficient of x2 in the expansion...Ch. 5.7 - 28. Determine the coefficient in the expansion of...Ch. 5.7 - 29. Determine the coefficient of in binomial...Ch. 5.7 - 30. Determine the coefficient of in the binomial...Ch. 5.7 - Determine the first three terms in the binomial...Ch. 5.7 - 32. Determine the last three terms in the binomial...Ch. 5.7 - 33. Determine the middle term in the binomial...Ch. 5.7 - Determine the coefficient of x4y2 in the binomial...Ch. 5.7 - Prob. 35ECh. 5.7 - 36. Determine the term containing in the...Ch. 5.7 - Prob. 37ECh. 5.7 - 38. How many different subsets can be chosen from...Ch. 5.7 - Restaurant Tip How many different tips could you...Ch. 5.7 - 40. Pizza Options A pizza parlor offers mushrooms,...Ch. 5.7 - Cable TV Options A cable TV franchise offers 20...Ch. 5.7 - 42. Salad Options A salad bar offers a base of...Ch. 5.7 - Tie Selection In how many ways can a selection of...Ch. 5.7 - Dessert Choices In how many ways can a selection...Ch. 5.7 - Prob. 45ECh. 5.7 - Ice Cream Sundaes An ice cream parlor offers four...Ch. 5.7 - 47. Appetizer Selection In how many ways can a...Ch. 5.7 - CD Selection In how many ways can a selection of...Ch. 5.7 - Lab Projects Students in a physics class are...Ch. 5.7 - 50. Election A voter is asked to vote for at most...Ch. 5.7 - CD Selection James has nine jazz CDs and ten top...Ch. 5.7 - Book Selection Sarah has five nonfiction and six...Ch. 5.7 - 53. Can be a term of a binomial expansion?
Ch. 5.7 - Can (85)x3 be a term of a binomial expansion?Ch. 5.7 - Prob. 55ECh. 5.7 - (a) Use equation (3) to show that...Ch. 5.7 - Find a simple expression for the value of...Ch. 5.7 - 58. Seating Passengers A blue van and a red van,...Ch. 5.8 - 1. A foundation wishes to award one grant of...Ch. 5.8 - 2. In how many different ways can six medical...Ch. 5.8 - Prob. 1ECh. 5.8 - Prob. 2ECh. 5.8 - Prob. 3ECh. 5.8 - Prob. 4ECh. 5.8 - Let S be a set of n elements. Determine the number...Ch. 5.8 - Let S be a set of n elements. Determine the number...Ch. 5.8 - Prob. 7ECh. 5.8 - Prob. 8ECh. 5.8 - Prob. 9ECh. 5.8 - Prob. 10ECh. 5.8 - Prob. 11ECh. 5.8 - Let S be a set of n elements. Determine the number...Ch. 5.8 - Prob. 13ECh. 5.8 - Prob. 14ECh. 5.8 - 15. Stock Reports A brokerage house regularly...Ch. 5.8 - 16. Investment Ratings An investment advisory...Ch. 5.8 - 17. RIFFRAFF How many eight-letter words consist...Ch. 5.8 - RAZZMATAZZ How many 10-letter words consist of one...Ch. 5.8 - 19. Postage Stamps In how many ways can three...Ch. 5.8 - 20. Nautical Signals A nautical signal consists of...Ch. 5.8 - 21. Observation Groups A psychology experiment...Ch. 5.8 - 22. Orientation Groups During orientation, new...Ch. 5.8 - 23. Weather In a certain month (of 30 days) it...Ch. 5.8 - Awarding Prizes Of the nine contestants in a...Ch. 5.8 - Job Promotions A corporation has four employees...Ch. 5.8 - 26. Forming Committees The 10 members of a city...Ch. 5.8 - 27. Field Trip In how many ways can the 14...Ch. 5.8 - 28. Work Schedule A sales representative must...Ch. 5.8 - 29. Basketball Teams Ten students in a physical...Ch. 5.8 - Sorting Sweaters In how many ways can 12 sweaters...Ch. 5.8 - Prob. 31ECh. 5.8 - Prob. 32ECh. 5.8 - Prob. 33ECh. 5.8 - 34. Campaign Tasks Calculate the number of ways...Ch. 5.8 - Prob. 35ECh. 5 - Prob. 1FCCECh. 5 - Prob. 2FCCECh. 5 - Prob. 3FCCECh. 5 - Define a universal set.Ch. 5 - 5. Define the empty set.
Ch. 5 - Prob. 6FCCECh. 5 - Prob. 7FCCECh. 5 - Prob. 8FCCECh. 5 - Prob. 9FCCECh. 5 - Prob. 10FCCECh. 5 - Prob. 11FCCECh. 5 - Prob. 12FCCECh. 5 - Prob. 13FCCECh. 5 - Prob. 14FCCECh. 5 - Prob. 15FCCECh. 5 - Prob. 16FCCECh. 5 - 17. Explain what is meant by an ordered partition...Ch. 5 - Prob. 18FCCECh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - 4. Team Picture In how many ways can a coach and...Ch. 5 - Prob. 5RECh. 5 - Determine the first three terms in the binomial...Ch. 5 - Balls in an Urn An urn contains 14 numbered balls,...Ch. 5 - 8. Testing a Drug Sixty people with a certain...Ch. 5 - 9. Appliance Purchase An appliance store carries...Ch. 5 - 10. Contest Prizes There are 12 contestants in a...Ch. 5 - 11. Languages Out of a group of 115 applicants for...Ch. 5 - Calculate (1715).Ch. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - Prob. 19RECh. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - 21. Nine-Letter Words How many different...Ch. 5 - Prob. 22RECh. 5 - Winter Sports A survey at a small New England...Ch. 5 - 24. Meal Choices How many different meals can be...Ch. 5 - 25. Test Scoring On an essay test, there are five...Ch. 5 - 26. Seven-Digit Numbers How many seven-digit...Ch. 5 - Telephone Numbers How many telephone numbers are...Ch. 5 - Three-Digit Numbers How many three-digit numbers...Ch. 5 - Eight-Letter Words How many strings of length 8...Ch. 5 - Basketball Teams How many different five-person...Ch. 5 - 31. Selecting Students Fourteen students in the...Ch. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Filling Jobs Sixty people apply for 10 job...Ch. 5 - Generating Tests A computerized test generator can...Ch. 5 - 36. Six-Letter Words If a string of six letters...Ch. 5 - 37. Choosing Delegations How many different...Ch. 5 - Prob. 38RECh. 5 - Distributing Candy In how many ways can 14...Ch. 5 - Prob. 40RECh. 5 - Prob. 41RECh. 5 - 42. Softball League If every team in a 10-team...Ch. 5 - Diagonals How many diagonals does an n-sided...Ch. 5 - 44. Racetrack Betting Racetracks have a compound...Ch. 5 - Prob. 45RECh. 5 - Prob. 46RECh. 5 - Prob. 47RECh. 5 - Poker How many hands of five cards contain exactly...Ch. 5 - Three-Digit Numbers How many three-digit numbers...Ch. 5 - 50. Three-Digit Numbers How many three-digit...Ch. 5 - Baseball In Exercises 51 and 52, suppose there are...Ch. 5 - Baseball In Exercises 51 and 52, suppose there are...Ch. 5 - Greek-Letter Societies Fraternity and sorority...Ch. 5 - 54. Family Picture A family consisting of two...Ch. 5 - Prob. 55RECh. 5 - 56. Splitting Classes Two elementary school...Ch. 5 - Prob. 57RECh. 5 - Arranging Books A set of books can be arranged on...Ch. 5 - Batting Order How many batting orders are possible...Ch. 5 - 60. Choosing Committees In the United States...Ch. 5 - Voting Suppose that you are voting in an election...Ch. 5 - Spelling Algebra The object is to start with the...Ch. 5 - Prob. 63RECh. 5 - Prob. 64RECh. 5 - Prob. 65RECh. 5 - Prob. 66RECh. 5 - Prob. 67RECh. 5 - Prob. 68RECh. 5 - Prob. 69RECh. 5 - Prob. 70RECh. 5 - Prob. 71RECh. 5 - Prob. 72RECh. 5 - Prob. 73RECh. 5 - Prob. 74RECh. 5 - 75. Express in your own words the difference...Ch. 5 - Prob. 76RECh. 5 - Prob. 77RECh. 5 - Prob. 78RECh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - In the following triangular table, known as...Ch. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9P
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- 6. Let P be the standard normal distribution, i.e., P is the proba- bility measure on (R, B(R)) given by 1 dP(x) = 를 = e dx. √2πT Consider the random variables 21 fn(x) = (1 + x²) en+2, x Є R, n Є N. Using the dominated convergence theorem, prove that the limit Total marks 9 exists and find it. lim E(fn) n∞ [9 Marks]arrow_forwardRefer to page 38 for solving an optimal control problem using dynamic programming. Instructions: • Define the value function and derive the Hamilton-Jacobi-Bellman (HJB) equation. • Solve the HJB equation explicitly, showing all intermediate steps and justifications. Verify the solution satisfies the boundary conditions and optimality. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 18 for solving a second-order linear non-homogeneous differential equation. Instructions: Solve the associated homogeneous equation first. Use either the method of undetermined coefficients or variation of parameters for the particular solution. • Provide detailed steps for combining solutions into the general solution. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forward
- 6. Let X be a random variable taking values in (0,∞) with proba- bility density function fx(u) = 5e5u u > 0. Total marks 8 Let Y = X2. Find the probability density function of Y. [8 Marks]arrow_forward5. Let a probability measure P on ([0,3], B([0,3])) be given by 1 dP(s): = ½ s² ds. 9 Consider a random variable X : [0,3] → R given by X(s) = s², sc [0,3]. S Total marks 7 Find the distribution of X. [7 Marks]arrow_forwardRefer to page 24 for solving a differential equation using Laplace transforms. Instructions: Take the Laplace transform of the given equation, applying initial conditions appropriately. ⚫ Solve the resulting algebraic equation and find the inverse transform. Provide step-by-step solutions with intermediate results and final verification. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forward
- Refer to page 30 for deriving the Euler-Lagrange equation for an optimal control problem. Instructions: • Use the calculus of variations to derive the Euler-Lagrange equation. Clearly define the functional being minimized or maximized. Provide step-by-step derivations, including all necessary boundary conditions. Avoid skipping critical explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 32 for solving a linear-quadratic regulator (LQR) problem. Instructions: • Formulate the cost functional and state-space representation. • Derive the Riccati equation and solve it step-by-step. Clearly explain how the optimal control law is obtained. Ensure all matrix algebra is shown in detail. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 14 for solving a linear first-order differential equation. Instructions: • Convert the equation into its standard linear form. • Use integrating factors to find the solution. Show all steps explicitly, from finding the factor to integrating and simplifying the solution. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
- Refer to page 10 for a problem involving solving an exact differential equation. Instructions: • Verify if the equation is exact by testing әм მყ - ƏN მე If not exact, determine an integrating factor to make it exact. • Solve step-by-step, showing all derivations. Avoid irrelevant explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Haz b9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 10 for a problem involving solving an exact differential equation. Instructions: Verify exactness carefully. ⚫ If the equation is not exact, find an integrating factor to make it exact. Solve step-by-step and ensure no algebraic steps are skipped. Provide detailed explanations for each transformation. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 34 for deriving and applying Pontryagin's Maximum Principle. Instructions: ⚫ Define the Hamiltonian for the given control problem. • • Derive the necessary conditions for optimality step-by-step, including state and co-state equations. Solve the resulting system of equations explicitly, showing all intermediate steps. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
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