>LCPO< FUND OF STATISTICS
5th Edition
ISBN: 9781034509998
Author: Sullivan
Publisher: PEARSON
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Chapter 5.4, Problem 30AYU
Golf Balls The local golf store sells an “onion bag” that contains 30 “experienced” golf balls. Suppose that the bag contains 20 Titleists, 8 Maxfis, and 7 Top-Fites. Use a tree diagram like the one in Example 5 to answer the following:
- a. What is the
probability that two randomly selected golf balls are both Titleists? - b. What is the probability that the first ball selected is a Titleist and the second is a Maxfis?
- c. What is the probability that the first ball selected is a Maxfis and the second is a Titleist?
- d. What is the probability that one golf ball is a Titleist and the other is a Maxfis?
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1 No.
2
3
4
Binomial Prob.
X
n
P
Answer
5
6 4
7
8
9
10
12345678
8
3
4
2
2552
10
0.7
0.233
0.3
0.132
7
0.6
0.290
20
0.02
0.053
150
1000
0.15
0.035
8
7
10
0.7
0.383
11
9
3
5
0.3
0.132
12
10
4
7
0.6
0.290
13
Poisson Probability
14
X
lambda
Answer
18 4
19
20
21
22
23 9
15
16
17 3
1234567829
3
2
0.180
2
1.5
0.251
12
10
0.095
5
3
0.101
7
4
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0.180
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step by step on Microssoft on how to put this in excel and the answers please
Find binomial probability if:
x = 8, n = 10, p = 0.7
x= 3, n=5, p = 0.3
x = 4, n=7, p = 0.6
Quality Control: A factory produces light bulbs with a 2% defect rate. If a random sample of 20 bulbs is tested, what is the probability that exactly 2 bulbs are defective? (hint: p=2% or 0.02; x =2, n=20; use the same logic for the following problems)
Marketing Campaign: A marketing company sends out 1,000 promotional emails. The probability of any email being opened is 0.15. What is the probability that exactly 150 emails will be opened? (hint: total emails or n=1000, x =150)
Customer Satisfaction: A survey shows that 70% of customers are satisfied with a new product. Out of 10 randomly selected customers, what is the probability that at least 8 are satisfied? (hint: One of the keyword in this question is “at least 8”, it is not “exactly 8”, the correct formula for this should be = 1- (binom.dist(7, 10, 0.7,…
Kate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). What is an example of fair division of the cake
S1
S2
S3
S4
Kate
$4.00
$6.00
$6.00
$4.00
Luke
$5.30
$5.00
$5.25
$5.45
Mary
$4.25
$4.50
$3.50
$3.75
Nancy
$6.00
$4.00
$4.00
$6.00
Chapter 5 Solutions
>LCPO< FUND OF STATISTICS
Ch. 5.1 - What is the probability of an event that is...Ch. 5.1 - What does it mean for an event to be unusual? Why...Ch. 5.1 - True or False: In a probability model, the sum of...Ch. 5.1 - True or False: Probability is a measure of the...Ch. 5.1 - In probability, a(n) _____ is any process that can...Ch. 5.1 - NW 6. A(n) _____ is any collection of outcomes...Ch. 5.1 - Verify that the table in the next column is a...Ch. 5.1 - Verify that the following is a probability model....Ch. 5.1 - Why is the following not a probability model?...Ch. 5.1 - Why is the following not a probability model?...
Ch. 5.1 - Which of the following numbers could be the...Ch. 5.1 - Which of the following numbers could be the...Ch. 5.1 - According to Nate Silver, the probability of a...Ch. 5.1 - In seven-card stud poker, a player is dealt seven...Ch. 5.1 - Suppose that you toss a coin 100 times and get 95...Ch. 5.1 - Suppose that you roll a die 100 times and get six...Ch. 5.1 - Bob is asked to construct a probability model for...Ch. 5.1 - NW 18. Blood Types A person can have one of four...Ch. 5.1 - If a person rolls a six-sided die and then flips a...Ch. 5.1 - If a basketball player shoots three free throws,...Ch. 5.1 - According to the U.S. Department of Education,...Ch. 5.1 - According to the American Veterinary Medical...Ch. 5.1 - let the sample space be S =...Ch. 5.1 - let the sample space be S =...Ch. 5.1 - let the sample space be S =...Ch. 5.1 - let the sample space be S =...Ch. 5.1 - Play Sports? A survey of 500 randomly selected...Ch. 5.1 - Volunteer? In a survey of 1100 female adults (18...Ch. 5.1 - NW 29. Home Runs The Wall Street Journal regularly...Ch. 5.1 - Planting Tulips A bag of 100 tulip bulbs purchased...Ch. 5.1 - Roulette In the game of roulette, a wheel consists...Ch. 5.1 - Birthdays Exclude leap years from the following...Ch. 5.1 - Genetics A gene is composed of two alleles, either...Ch. 5.1 - More Genetics In Problem 33, we learned that for...Ch. 5.1 - NW 35. College Survey In a national survey...Ch. 5.1 - College Survey In a national survey conducted by...Ch. 5.1 - Larceny Theft A police officer randomly selected...Ch. 5.1 - Multiple Births The following data represent the...Ch. 5.1 - In Problems 3942, use the given table, which lists...Ch. 5.1 - Prob. 40AYUCh. 5.1 - In Problems 3942, use the given table, which lists...Ch. 5.1 - In Problems 3942, use the given table, which lists...Ch. 5.1 - Going to Disney World John, Roberto, Clarice,...Ch. 5.1 - Six Flags In 2011, Six Flags St. Louis had 10...Ch. 5.1 - Prob. 45AYUCh. 5.1 - Prob. 46AYUCh. 5.1 - NW 47. Simulation Use a graphing calculator or...Ch. 5.1 - Classifying Probability Determine whether the...Ch. 5.1 - Prob. 49AYUCh. 5.1 - Prob. 51AYUCh. 5.1 - The middle 50% of enrolled freshmen at Washington...Ch. 5.1 - NFL Combine Each year the National Football League...Ch. 5.1 - Putting It Together: Drug Side Effects In...Ch. 5.1 - Prob. 55AYUCh. 5.1 - In computing classical probabilities, all outcomes...Ch. 5.1 - Describe what an unusual event is. Should the same...Ch. 5.1 - Prob. 58AYUCh. 5.1 - Describe the difference between classical and...Ch. 5.1 - Prob. 60AYUCh. 5.1 - Suppose you live in a town with two hospitalsone...Ch. 5.2 - What does it mean when two events are disjoint?Ch. 5.2 - If E and F are disjoint events, then P(E or F) =...Ch. 5.2 - If E and F are not disjoint events, then P(E or F)...Ch. 5.2 - What does it mean when two events are complements?Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - If P (E) = 0.60, P (E or F) = 0.85, and P (E and...Ch. 5.2 - Prob. 20AYUCh. 5.2 - In Problems 2124, a golf ball is selected at...Ch. 5.2 - In Problems 2124, a golf ball is selected at...Ch. 5.2 - In Problems 2124, a golf ball is selected at...Ch. 5.2 - In Problems 2124, a golf ball is selected at...Ch. 5.2 - Weapon of Choice The following probability model...Ch. 5.2 - Family Structure The following probability model...Ch. 5.2 - If events E and F are disjoint and the events F...Ch. 5.2 - Draw a Venn diagram like that in Figure 10 that...Ch. 5.2 - Medicare Fines In an effort to reduce the number...Ch. 5.2 - Housing The following data represents the number...Ch. 5.2 - A Deck of Cards A standard deck of cards contains...Ch. 5.2 - A Deck of Cards A standard deck of cards contains...Ch. 5.2 - Birthdays Exclude leap years from the following...Ch. 5.2 - Roulette In the game of roulette, a wheel consists...Ch. 5.2 - Health Problems According to the Centers for...Ch. 5.2 - Visits to the Doctor A National Ambulatory Medical...Ch. 5.2 - Language Spoken at Home According to the U.S....Ch. 5.2 - Getting to Work According to the U.S. Census...Ch. 5.2 - Cigar Smoking The data in the table in the next...Ch. 5.2 - Working Couples A guidance counselor at a middle...Ch. 5.2 - The Placebo Effect A company is testing a new...Ch. 5.2 - Social Media Harris Interactive conducted a survey...Ch. 5.2 - Driver Fatalities The following data represent the...Ch. 5.2 - Prob. 44AYUCh. 5.2 - Putting It Together: Red Light Cameras In a study...Ch. 5.2 - Exam Scores The following data represent the...Ch. 5.3 - Two events E and F are _____ if the occurrence of...Ch. 5.3 - The word and in probability implies that we use...Ch. 5.3 - The word or in probability implies that we use the...Ch. 5.3 - True or False: When two events are disjoint, they...Ch. 5.3 - If two events E and F are independent, P (E and F)...Ch. 5.3 - Suppose events E and F are disjoint. What is P(E...Ch. 5.3 - Determine whether the events E and F are...Ch. 5.3 - Determine whether the events E and F are...Ch. 5.3 - Suppose that events E and F are independent, P (E)...Ch. 5.3 - Suppose that events E and F are independent, P (E)...Ch. 5.3 - Flipping a Coin What is the probability of...Ch. 5.3 - Rolling a Die What is the probability of obtaining...Ch. 5.3 - Southpaws About 13% of the population is...Ch. 5.3 - Double Jackpot Shawn lives near the border of...Ch. 5.3 - False Positives The ELISA is a test to determine...Ch. 5.3 - Prob. 16AYUCh. 5.3 - Life Expectancy The probability that a randomly...Ch. 5.3 - Life Expectancy The probability that a randomly...Ch. 5.3 - Derivatives In finance, a derivative is a...Ch. 5.3 - Quality Control Suppose that a company selects two...Ch. 5.3 - Reliability and Redundancy In airline...Ch. 5.3 - Reliability For a parallel structure of identical...Ch. 5.3 - Prob. 23AYUCh. 5.3 - Cold Streaks Players in sports are said to have...Ch. 5.3 - Bowling Suppose that Ralph gets a strike when...Ch. 5.3 - Driving under the Influence Among 21- to...Ch. 5.3 - Prob. 27AYUCh. 5.3 - Audits and Pet Ownership According to Internal...Ch. 5.3 - Weight Gain and Gender According to the National...Ch. 5.3 - Stocks Suppose your financial advisor recommends...Ch. 5.3 - Betting on Sports According to a Gallup Poll,...Ch. 5.3 - Prob. 32AYUCh. 5.3 - Prob. 33AYUCh. 5.3 - Prob. 34AYUCh. 5.4 - The notation P(F|E) means the probability of event...Ch. 5.4 - If P (E) = 0,6 and P(E\F) = 0.34, are events E and...Ch. 5.4 - Prob. 3AYUCh. 5.4 - Suppose that E and F are two events and that P(E...Ch. 5.4 - Suppose that E and F are two events and that N(E...Ch. 5.4 - Suppose that E and F are two events and that N...Ch. 5.4 - Suppose that E and F are two events and that P (E)...Ch. 5.4 - Prob. 8AYUCh. 5.4 - According to the U.S. Census Bureau, the...Ch. 5.4 - Prob. 10AYUCh. 5.4 - Drawing a Card Suppose that a single card is...Ch. 5.4 - Prob. 12AYUCh. 5.4 - Rainy Days For the month of June in the city of...Ch. 5.4 - Cause of Death According to the U.S. National...Ch. 5.4 - High School Dropouts According to the U.S. Census...Ch. 5.4 - Income by Region According to the U.S. Census...Ch. 5.4 - Made in America In a recent Harris Poll, a random...Ch. 5.4 - Social Media Adult Americans (18 years or older)...Ch. 5.4 - Driver Fatalities The following data represent the...Ch. 5.4 - Speeding Tickets Use the results of Problem 44 in...Ch. 5.4 - Acceptance Sampling Suppose that you just received...Ch. 5.4 - Committee A committee consisting of four women and...Ch. 5.4 - Suppose that two cards are randomly selected from...Ch. 5.4 - Suppose that two cards are randomly selected from...Ch. 5.4 - Board Work This past semester, I had a small...Ch. 5.4 - Party My wife has organized a monthly neighborhood...Ch. 5.4 - Playing Music on Random Setting Suppose that a...Ch. 5.4 - Packaging Error Because of a manufacturing error,...Ch. 5.4 - Planting Tulips A bag of 30 tulip bulbs purchased...Ch. 5.4 - Golf Balls The local golf store sells an onion bag...Ch. 5.4 - Smokers According to the National Center for...Ch. 5.4 - Prob. 32AYUCh. 5.4 - The Birthday Problem Determine the probability...Ch. 5.4 - The Birthday Problem Using the procedure given in...Ch. 5.4 - Prob. 35AYUCh. 5.4 - Party Affiliation The following data represent...Ch. 5.4 - A Flush A flush in the card game of poker occurs...Ch. 5.4 - Prob. 38AYUCh. 5.4 - Independence in Small Samples from Large...Ch. 5.4 - Independence in Small Samples from Large...Ch. 5.4 - Prob. 41AYUCh. 5.4 - Prob. 42AYUCh. 5.5 - A _____ is an ordered arrangement of r objects...Ch. 5.5 - A _____ is an arrangement of r objects chosen from...Ch. 5.5 - True or False: In a combination problem, order is...Ch. 5.5 - The factorial symbol, n!, is defined as n! _____...Ch. 5.5 - In Problems 510, find the value of each factorial....Ch. 5.5 - In Problems 510, find the value of each factorial....Ch. 5.5 - In Problems 510, find the value of each factorial....Ch. 5.5 - In Problems 510, find the value of each factorial....Ch. 5.5 - Prob. 9AYUCh. 5.5 - Prob. 10AYUCh. 5.5 - In Problems 1118, find the value of each...Ch. 5.5 - Prob. 12AYUCh. 5.5 - In Problems 1118, find the value of each...Ch. 5.5 - In Problems 1118, find the value of each...Ch. 5.5 - Prob. 15AYUCh. 5.5 - Prob. 16AYUCh. 5.5 - Prob. 17AYUCh. 5.5 - In Problems 1118, find the value of each...Ch. 5.5 - In Problems 1926, find the value of each...Ch. 5.5 - In Problems 1926, find the value of each...Ch. 5.5 - Prob. 21AYUCh. 5.5 - Prob. 22AYUCh. 5.5 - Prob. 23AYUCh. 5.5 - Prob. 24AYUCh. 5.5 - Prob. 25AYUCh. 5.5 - In Problems 1926, find the value of each...Ch. 5.5 - List all the permutations of five objects a, b, c,...Ch. 5.5 - List all the permutations of four objects a, b, c,...Ch. 5.5 - List all the combinations of five objects a, b, c,...Ch. 5.5 - Prob. 30AYUCh. 5.5 - Clothing Options A man has six shirts and four...Ch. 5.5 - Prob. 32AYUCh. 5.5 - Prob. 33AYUCh. 5.5 - Arranging Students In how many ways can 15...Ch. 5.5 - Traveling Salesperson A salesperson must travel to...Ch. 5.5 - Prob. 36AYUCh. 5.5 - Prob. 37AYUCh. 5.5 - Stocks on the NASDAQ Companies whose stocks are...Ch. 5.5 - Garage Door Code Outside a home there is a keypad...Ch. 5.5 - Social Security Numbers A Social Security number...Ch. 5.5 - User Names Suppose that a local area network...Ch. 5.5 - User Names How many user names are possible in...Ch. 5.5 - Combination Locks A combination lock has 50...Ch. 5.5 - Forming License Plate Numbers How many different...Ch. 5.5 - INDY 500 Suppose 40 cars start at the Indianapolis...Ch. 5.5 - Betting on the Perfecta In how many ways can the...Ch. 5.5 - Forming a Committee Four members from a 20-person...Ch. 5.5 - Forming a Committee Four members from a 50-person...Ch. 5.5 - Lottery A lottery exists where balls numbered 125...Ch. 5.5 - Forming a Committee In the U.S. Senate, there are...Ch. 5.5 - Simple Random Sample How many different simple...Ch. 5.5 - Simple Random Sample How many different simple...Ch. 5.5 - Prob. 53AYUCh. 5.5 - Prob. 54AYUCh. 5.5 - DNA Sequences (See Example 10 on page 278.) How...Ch. 5.5 - Prob. 56AYUCh. 5.5 - Landscape Design A golf-course architect has four...Ch. 5.5 - Starting Lineup A baseball team consists of three...Ch. 5.5 - Prob. 59AYUCh. 5.5 - Mega Millions In Mega Millions, an urn contains...Ch. 5.5 - Selecting a Jury The grade appeal process at a...Ch. 5.5 - Selecting a Committee Suppose that there are 55...Ch. 5.5 - Acceptance Sampling Suppose that a shipment of 120...Ch. 5.5 - In the Dark A box containing twelve 40-watt light...Ch. 5.5 - Randomly Playing Songs Suppose a playlist you just...Ch. 5.5 - Packaging Error Through a manufacturing error,...Ch. 5.5 - Prob. 67AYUCh. 5.5 - Two of a Kind Follow the outline presented in...Ch. 5.5 - Prob. 69AYUCh. 5.5 - Acceptance Sampling Suppose that you have just...Ch. 5.5 - Password Policy According to the Sefton Council...Ch. 5.6 - What is the difference between a permutation and a...Ch. 5.6 - What method of assigning probabilities to a simple...Ch. 5.6 - Prob. 3AYUCh. 5.6 - Prob. 4AYUCh. 5.6 - Prob. 5AYUCh. 5.6 - Prob. 6AYUCh. 5.6 - Prob. 7AYUCh. 5.6 - Prob. 8AYUCh. 5.6 - Prob. 9AYUCh. 5.6 - Prob. 10AYUCh. 5.6 - In Problems 1012, evaluate each expression. 11....Ch. 5.6 - In Problems 1012, evaluate each expression. 12....Ch. 5.6 - Suppose that events E and F are independent. P (E)...Ch. 5.6 - Prob. 14AYUCh. 5.6 - Prob. 16AYUCh. 5.6 - Soccer? In a survey of 500 randomly selected...Ch. 5.6 - Apartment Vacancy A real estate agent conducted a...Ch. 5.6 - Prob. 19AYUCh. 5.6 - Starting Lineups Paytons futsal team consists of...Ch. 5.6 - Titanic Survivors The following data represent the...Ch. 5.6 - Marijuana Use According to the Statistical...Ch. 5.6 - Prob. 23AYUCh. 5.6 - National Honor Society The distribution of...Ch. 5.6 - Instant Winner In 2002, Valerie Wilson won 1...Ch. 5.6 - Text Twist In the game Text Twist, six letters are...Ch. 5.6 - Marriage and Education According to the U.S....Ch. 5.6 - Weather Forecast The weather forecast says there...Ch. 5.6 - Essay Test An essay test in European History has...Ch. 5.6 - Exercise Routines Todd is putting together an...Ch. 5.6 - New Cars If the 2015 Hyundai Genesis has 2 engine...Ch. 5.6 - Lingo In the gameshow Lingo, the team that...Ch. 5 - (a) a. Which among the following numbers could be...Ch. 5 - For Problems 25, let the sample space be S = {red,...Ch. 5 - For Problems 25, let the sample space be S = {red,...Ch. 5 - For Problems 25, let the sample space be S = {red,...Ch. 5 - For Problems 25, let the sample space be S = {red,...Ch. 5 - Suppose that P (E) = 0.76, P (F) = 0.45, and P (E...Ch. 5 - Suppose that P (E) = 0.36, P (F) = 0.12, and E and...Ch. 5 - Suppose that events E and F are independent. In...Ch. 5 - Suppose that P (E) = 0.8, P (F) = 0.5, and P (E...Ch. 5 - Suppose that P (E) = 0.59 and P(F|E) = 0.45. What...Ch. 5 - Suppose that P (E and F) = 0.35 and P (F) = 0.7....Ch. 5 - Determine the value of each of the following: a....Ch. 5 - Roulette In the game of roulette, a wheel consists...Ch. 5 - Traffic Fatalities In 2013, there were 32.719...Ch. 5 - Long Life? In a poll conducted by Genworth...Ch. 5 - Gestation Period versus Weight The following data...Ch. 5 - Who Do You Trust? According to the National...Ch. 5 - Pick 3 For the Illinois Lotterys PICK 3 game, a...Ch. 5 - Prob. 19RECh. 5 - Drawing Cards Suppose that you draw 3 cards...Ch. 5 - Forming License Plates A license plate is designed...Ch. 5 - Prob. 22RECh. 5 - Arranging Flags How many different vertical...Ch. 5 - Prob. 24RECh. 5 - Arizonas Pick 5 In one of Arizonas lotteries,...Ch. 5 - Packaging Error Because of a mistake in packaging,...Ch. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Playing Five-Card Stud In the game of five-card...Ch. 5 - Prob. 30RECh. 5 - Lottery Luck In 1996, a New York couple won 2.5...Ch. 5 - Coffee Sales The following data represent the...Ch. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - For Problems 24, let the sample space be S =...Ch. 5 - For Problems 24, let the sample space be S =...Ch. 5 - Suppose that P (E) = 0.37 and P (F) = 0.22. a....Ch. 5 - Suppose that P (E) = 0.15, P (F) = 0.45, and...Ch. 5 - Determine the value of each of the following: a....Ch. 5 - Craps is a dice game in which two fair dice are...Ch. 5 - According to Gallup, 26% of adult Americans...Ch. 5 - The following probability model shows the...Ch. 5 - The following represent the results of a survey in...Ch. 5 - During the 2014 season, the Los Angeles Dodgers...Ch. 5 - You just received a shipment of 10 DVD players....Ch. 5 - Prob. 14CTCh. 5 - The U.S. Senate Appropriations Committee has 29...Ch. 5 - Prob. 16CTCh. 5 - Prob. 17CTCh. 5 - A survey distributed at the 28th Lunar and...Ch. 5 - How many distinguishable DNA sequences can be...Ch. 5 - A student is taking a 40-question multiple-choice...Ch. 5 - Offender is at least 18.Ch. 5 - Prob. 2CSCh. 5 - Prob. 3CSCh. 5 - Prob. 4CSCh. 5 - Prob. 5CSCh. 5 - Prob. 6CSCh. 5 - Prob. 7CSCh. 5 - Prob. 8CSCh. 5 - Prob. 9CSCh. 5 - Prob. 10CSCh. 5 - Prob. 11CSCh. 5 - Prob. 12CSCh. 5 - Prob. 13CSCh. 5 - Prob. 14CSCh. 5 - Prob. 15CSCh. 5 - Prob. 16CSCh. 5 - Prob. 17CSCh. 5 - Prob. 18CSCh. 5 - Prob. 19CSCh. 5 - Prob. 20CSCh. 5 - Prob. 21CSCh. 5 - Prob. 22CSCh. 5 - Prob. 23CSCh. 5 - Prob. 24CS
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- Question 3. We want to price a put option with strike price K and expiration T. Two financial advisors estimate the parameters with two different statistical methods: they obtain the same return rate μ, the same volatility σ, but the first advisor has interest r₁ and the second advisor has interest rate r2 (r1>r2). They both use a CRR model with the same number of periods to price the option. Which advisor will get the larger price? (Explain your answer.)arrow_forwardQuestion 5. We consider a put option with strike price K and expiration T. This option is priced using a 1-period CRR model. We consider r > 0, and σ > 0 very large. What is the approximate price of the option? In other words, what is the limit of the price of the option as σ∞. (Briefly justify your answer.)arrow_forwardQuestion 6. You collect daily data for the stock of a company Z over the past 4 months (i.e. 80 days) and calculate the log-returns (yk)/(-1. You want to build a CRR model for the evolution of the stock. The expected value and standard deviation of the log-returns are y = 0.06 and Sy 0.1. The money market interest rate is r = 0.04. Determine the risk-neutral probability of the model.arrow_forward
- Several markets (Japan, Switzerland) introduced negative interest rates on their money market. In this problem, we will consider an annual interest rate r < 0. We consider a stock modeled by an N-period CRR model where each period is 1 year (At = 1) and the up and down factors are u and d. (a) We consider an American put option with strike price K and expiration T. Prove that if <0, the optimal strategy is to wait until expiration T to exercise.arrow_forwardWe consider an N-period CRR model where each period is 1 year (At = 1), the up factor is u = 0.1, the down factor is d = e−0.3 and r = 0. We remind you that in the CRR model, the stock price at time tn is modeled (under P) by Sta = So exp (μtn + σ√AtZn), where (Zn) is a simple symmetric random walk. (a) Find the parameters μ and σ for the CRR model described above. (b) Find P Ste So 55/50 € > 1). StN (c) Find lim P 804-N (d) Determine q. (You can use e- 1 x.) Ste (e) Find Q So (f) Find lim Q 004-N StN Soarrow_forwardIn this problem, we consider a 3-period stock market model with evolution given in Fig. 1 below. Each period corresponds to one year. The interest rate is r = 0%. 16 22 28 12 16 12 8 4 2 time Figure 1: Stock evolution for Problem 1. (a) A colleague notices that in the model above, a movement up-down leads to the same value as a movement down-up. He concludes that the model is a CRR model. Is your colleague correct? (Explain your answer.) (b) We consider a European put with strike price K = 10 and expiration T = 3 years. Find the price of this option at time 0. Provide the replicating portfolio for the first period. (c) In addition to the call above, we also consider a European call with strike price K = 10 and expiration T = 3 years. Which one has the highest price? (It is not necessary to provide the price of the call.) (d) We now assume a yearly interest rate r = 25%. We consider a Bermudan put option with strike price K = 10. It works like a standard put, but you can exercise it…arrow_forward
- In this problem, we consider a 2-period stock market model with evolution given in Fig. 1 below. Each period corresponds to one year (At = 1). The yearly interest rate is r = 1/3 = 33%. This model is a CRR model. 25 15 9 10 6 4 time Figure 1: Stock evolution for Problem 1. (a) Find the values of up and down factors u and d, and the risk-neutral probability q. (b) We consider a European put with strike price K the price of this option at time 0. == 16 and expiration T = 2 years. Find (c) Provide the number of shares of stock that the replicating portfolio contains at each pos- sible position. (d) You find this option available on the market for $2. What do you do? (Short answer.) (e) We consider an American put with strike price K = 16 and expiration T = 2 years. Find the price of this option at time 0 and describe the optimal exercising strategy. (f) We consider an American call with strike price K ○ = 16 and expiration T = 2 years. Find the price of this option at time 0 and describe…arrow_forward2.2, 13.2-13.3) question: 5 point(s) possible ubmit test The accompanying table contains the data for the amounts (in oz) in cans of a certain soda. The cans are labeled to indicate that the contents are 20 oz of soda. Use the sign test and 0.05 significance level to test the claim that cans of this soda are filled so that the median amount is 20 oz. If the median is not 20 oz, are consumers being cheated? Click the icon to view the data. What are the null and alternative hypotheses? OA. Ho: Medi More Info H₁: Medi OC. Ho: Medi H₁: Medi Volume (in ounces) 20.3 20.1 20.4 Find the test stat 20.1 20.5 20.1 20.1 19.9 20.1 Test statistic = 20.2 20.3 20.3 20.1 20.4 20.5 Find the P-value 19.7 20.2 20.4 20.1 20.2 20.2 P-value= (R 19.9 20.1 20.5 20.4 20.1 20.4 Determine the p 20.1 20.3 20.4 20.2 20.3 20.4 Since the P-valu 19.9 20.2 19.9 Print Done 20 oz 20 oz 20 oz 20 oz ce that the consumers are being cheated.arrow_forwardT Teenage obesity (O), and weekly fast-food meals (F), among some selected Mississippi teenagers are: Name Obesity (lbs) # of Fast-foods per week Josh 185 10 Karl 172 8 Terry 168 9 Kamie Andy 204 154 12 6 (a) Compute the variance of Obesity, s²o, and the variance of fast-food meals, s², of this data. [Must show full work]. (b) Compute the Correlation Coefficient between O and F. [Must show full work]. (c) Find the Coefficient of Determination between O and F. [Must show full work]. (d) Obtain the Regression equation of this data. [Must show full work]. (e) Interpret your answers in (b), (c), and (d). (Full explanations required). Edit View Insert Format Tools Tablearrow_forward
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