Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 2.1, Problem 50E
To determine
To find:
The number of playing cards that fit the given description.
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Problem 1. Multi-stock model
We consider a 2-stock model similar to the one studied in class. Namely, we consider
=
S(1)
S(2)
=
S(¹) exp (σ1B(1) + (M1 - 0/1 )
S(²) exp (02B(2) + (H₂-
M2
where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with
t≥0
Cov (B(¹), B(2)) = p min{t, s}.
"
The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian
motion (W+)+20 (W(1), W(2))+20 such that
=
S(1)
S(2)
=
=
S(¹) exp (011W(¹) + (μ₁ - 01/1) t)
롱)
S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t).
where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p).
Hint: The constants will follow the formulas developed in the lectures.
(a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2)
functions of (B(1), B(²)).
as
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dimensional standard Brownian motion (i.e. show that each component is normal,
with mean 0, variance t, and that their…
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Chapter 2 Solutions
Mathematics: A Practical Odyssey
Ch. 2.1 - Prob. 1ECh. 2.1 - Suppose A={2,5,7,9,13,25,26}. a. Find n(A) b. True...Ch. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Suppose n(U)=150, n(A)=37, and n(B)=84. a. If...Ch. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.1 - Prob. 51ECh. 2.1 - Prob. 52ECh. 2.1 - Prob. 53ECh. 2.1 - Prove the Cardinal Number Rule for the Complement...Ch. 2.1 - Prob. 55ECh. 2.1 - Prob. 56ECh. 2.1 - Answer the following questions using complete...Ch. 2.1 - Prob. 58ECh. 2.1 - Prob. 59ECh. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Prob. 62ECh. 2.1 - Prob. 63ECh. 2.1 - Prob. 64ECh. 2.1 - Prob. 65ECh. 2.1 - Prob. 66ECh. 2.1 - Prob. 67ECh. 2.1 - Prob. 68ECh. 2.1 - The following questions are modeled after those...Ch. 2.2 - A survey of 200 people yielded the following...Ch. 2.2 - A survey of 300 workers yielded the following...Ch. 2.2 - The records of 1,492 high school graduates were...Ch. 2.2 - A department store surveyed 428 shoppers, and the...Ch. 2.2 - In a survey, 674 adults were asked what television...Ch. 2.2 - A survey asked 816 college freshmen whether they...Ch. 2.2 - A local 4-H club surveyed its members, and the...Ch. 2.2 - A local anime fan club surveyed its members...Ch. 2.2 - A recent survey of w shoppers that is, n(U)=w...Ch. 2.2 - A recent transportation survey of w urban...Ch. 2.2 - A consumer survey was conducted to examine...Ch. 2.2 - In a recent survey of monetary donations made by...Ch. 2.2 - Recently, Lady Gaga, Arcade Fire, and Skrillex had...Ch. 2.2 - Dr. Hawk works in an allergy clinic, and his...Ch. 2.2 - When the member of the Eye and I photo club...Ch. 2.2 - After leaving the polls, many people are asked how...Ch. 2.2 - In a recent survey consumer were asked where they...Ch. 2.2 - A company that specializes in language tutorial...Ch. 2.2 - In a recent survey, people were asked which radio...Ch. 2.2 - In a recent health insurance survey, employee at...Ch. 2.2 - A survey of 136 pet owners yielded the following...Ch. 2.2 - An exit poll of 300 votes yielded the following...Ch. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Using Venn diagrams, prove De Morgans law (AB)=AB.Ch. 2.2 - Prob. 34ECh. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Prob. 40ECh. 2.2 - If a person has type B blood, what blood types may...Ch. 2.2 - Prob. 42ECh. 2.2 - If a person has type O blood, what blood types may...Ch. 2.2 - Answer the following questions using complete...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Exercises 4652 refer to the following: A nonprofit...Ch. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Jamie has decided to buy either a Mega or a Better...Ch. 2.3 - Prob. 4ECh. 2.3 - If you buy three pairs of jeans, four sweaters,...Ch. 2.3 - A certain model of automobiles is available in six...Ch. 2.3 - To fulfill certain requirements for a degree, a...Ch. 2.3 - To fulfill a requirement for a literature class, a...Ch. 2.3 - A sporting goods store has fourteen lines of snow...Ch. 2.3 - An audio equipment store has ten different...Ch. 2.3 - A cafeteria offers a complete dinner that includes...Ch. 2.3 - A sandwich shop offers a U-Chooz special...Ch. 2.3 - How many different Social Security numbers are...Ch. 2.3 - To use an automated teller machine ATM, a customer...Ch. 2.3 - Every book published has an International Standard...Ch. 2.3 - How many different Zip Codes are possible using a...Ch. 2.3 - Telephone area codes are three-digit numbers of...Ch. 2.3 - Major credit cards such as VISA and MasterCard...Ch. 2.3 - The serial number on a dollar bill consists of a...Ch. 2.3 - The serial number on a new twenty-dollar bill...Ch. 2.3 - Each student at State University has a student ID...Ch. 2.3 - Each student at State College has a student ID...Ch. 2.3 - In Exercises 2338, find the indicated value. 4!Ch. 2.3 - In Exercises 2338, find the indicated value. 5!Ch. 2.3 - In Exercises 2338, find the indicated value. 10!Ch. 2.3 - In Exercises 2338, find the indicated value. 8!Ch. 2.3 - In Exercises 2338, find the indicated value. 20!Ch. 2.3 - In Exercises 2338, find the indicated value. 25!Ch. 2.3 - In Exercises 2338, find the indicated value. 6!4!Ch. 2.3 - In Exercises 2338, find the indicated value. 8!6!Ch. 2.3 - In Exercises 2338, find the indicated value. a....Ch. 2.3 - In Exercises 2338, find the indicated value. a....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - Find the value of n!(nr)!, when n=16 and r=14.Ch. 2.3 - Find the value of n!(nr)!, when n=19 and r=16.Ch. 2.3 - Find the value of n!(nr)!, when n=5 and r=5.Ch. 2.3 - Find the value of n!(nr)!, when n=r.Ch. 2.3 - Find the value of n!(nr)!r!, when n=7 and r=3.Ch. 2.3 - Find the value of n!(nr)!r!, when n=7 and r=4.Ch. 2.3 - Find the value of n!(nr)!r!, when n=5 and r=5.Ch. 2.3 - Find the value of n!(nr)!r!, when n=r.Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - The following questions are modeled after those...Ch. 2.3 - Prob. 51ECh. 2.3 - The following questions are modeled after those...Ch. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.4 - In Exercises 112, find the indicated value: a. 7P3...Ch. 2.4 - In Exercises 112, find the indicated value: a. 8P4...Ch. 2.4 - In Exercises 112, find the indicated value: a. 5P5...Ch. 2.4 - In Exercises 112, find the indicated value: a. 9P0...Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a. xP1...Ch. 2.4 - In Exercises 112, find the indicated value: a. xP2...Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - a. Find 3P2. b. List all of the permutations of...Ch. 2.4 - a. Find 3C2. b. List all of the combinations of...Ch. 2.4 - Prob. 15ECh. 2.4 - a. Find 4P2. b. List all of the permutations of...Ch. 2.4 - Prob. 17ECh. 2.4 - An English class consists of twenty-three students...Ch. 2.4 - In how many ways can the letters in the word...Ch. 2.4 - A committee of four is to be selected from a group...Ch. 2.4 - A softball league has thirteen teams. If every...Ch. 2.4 - In a group of eighteen people, each person shakes...Ch. 2.4 - A softball league has thirteen teams. How many...Ch. 2.4 - Three hundred people buy raffle tickets. Three...Ch. 2.4 - A group of nine women and six men must select a...Ch. 2.4 - A group of ten seniors, eight juniors, six...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - How many five-card poker hands containing two pair...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - A 5/36 lottery requires choosing five of the...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Over forty states participate in Powerball, a...Ch. 2.4 - Over forty states participate in Mega Millions, a...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - a. Find the sum of the entries in the first row of...Ch. 2.4 - a. Add adjacent entries of the sixth row of...Ch. 2.4 - Use Pascals Triangle to answer the following. a....Ch. 2.4 - Given the set S={a, b, c, d}, answer the...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercises 49-56, find the number of permutation...Ch. 2.4 - In Exercises 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutations...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - Prob. 61ECh. 2.4 - Prob. 62ECh. 2.4 - Exercise 6367 refer to the following: A baseball...Ch. 2.4 - Prob. 64ECh. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.5 - Prob. 1ECh. 2.5 - In Exercises 1-10, find the cardinal numbers of...Ch. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Consider the following one-to-one correspondence...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.CR - Prob. 1CRCh. 2.CR - Prob. 2CRCh. 2.CR - Prob. 3CRCh. 2.CR - Prob. 4CRCh. 2.CR - Prob. 5CRCh. 2.CR - Prob. 6CRCh. 2.CR - Prob. 7CRCh. 2.CR - Prob. 8CRCh. 2.CR - Prob. 9CRCh. 2.CR - A survey of 1,000 college seniors yielded the...Ch. 2.CR - A survey of recent college graduates yielded the...Ch. 2.CR - A local anime fan club surveyed 67 of its members...Ch. 2.CR - An exit poll yielded following information...Ch. 2.CR - Prob. 14CRCh. 2.CR - Prob. 15CRCh. 2.CR - Prob. 16CRCh. 2.CR - Prob. 17CRCh. 2.CR - A certain model of pickup truck is available in...Ch. 2.CR - Each student at State University has a student ID...Ch. 2.CR - Prob. 20CRCh. 2.CR - Prob. 21CRCh. 2.CR - Prob. 22CRCh. 2.CR - A group of ten women and twelve men must select a...Ch. 2.CR - Prob. 24CRCh. 2.CR - Prob. 25CRCh. 2.CR - Using a standard deck of fifty-two cards no...Ch. 2.CR - Prob. 27CRCh. 2.CR - A 6/42 lottery requires choosing six of the...Ch. 2.CR - Prob. 29CRCh. 2.CR - Prob. 30CRCh. 2.CR - Prob. 31CRCh. 2.CR - Prob. 32CRCh. 2.CR - Prob. 33CRCh. 2.CR - Prob. 34CRCh. 2.CR - Prob. 35CRCh. 2.CR - Prob. 36CRCh. 2.CR - Prob. 37CRCh. 2.CR - Consider the following one to one correspondence...Ch. 2.CR - Prob. 39CRCh. 2.CR - Prob. 40CRCh. 2.CR - Prob. 41CRCh. 2.CR - Prob. 42CRCh. 2.CR - Prob. 43CRCh. 2.CR - Prob. 44CRCh. 2.CR - Prob. 45CRCh. 2.CR - Prob. 46CRCh. 2.CR - Prob. 47CRCh. 2.CR - Prob. 48CR
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