Elementary Statistics (13th Edition)
13th Edition
ISBN: 9780134462455
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 4.1, Problem 2BSC
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A random variable X takes values 0 and 1 with probabilities q and p, respectively, with q+p=1. find the moment generating function of X and show that all the moments about the origin equal p. (Note- Please include as much detailed solution/steps in the solution to understand, Thank you!)
1 (Expected Shortfall)
Suppose the price of an asset Pt follows a normal random walk, i.e., Pt =
Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²).
Po+r1+.
⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price
in T days, i.e., VaRq(Pt – Pt–T).
-
• If ESq(rt) = A, find ES₁(Pt – Pt–T).
2 (Normal Distribution)
Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47).
What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3?
What is P(rt (4) < 2)?
What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13?
• What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given
rt-2 = 0.6?
Chapter 4 Solutions
Elementary Statistics (13th Edition)
Ch. 4.1 - New Jersey Lottery Let A denote the event of...Ch. 4.1 - Probability Rewrite the following statement so...Ch. 4.1 - Interpreting Weather While this exercise was being...Ch. 4.1 - Subjective Probability Estimate the probability...Ch. 4.1 - Identifying Probability Values Which of the...Ch. 4.1 - Penicillin Who discovered penicillin: Sean Penn,...Ch. 4.1 - Avogadro Constant If you are asked on a quiz to...Ch. 4.1 - Births Example 2 in this section includes the...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...
Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - SAT Test When making a random guess for an answer...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - Randomness When using a computer to randomly...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Kentucky Pick 4 In the Kentucky Pick 4 lottery,...Ch. 4.1 - Finding Odds in Roulette A roulette wheel has 38...Ch. 4.1 - Kentucky Derby Odds When the horse California...Ch. 4.1 - Relative Risk and Odds Ratio In a clinical trial...Ch. 4.2 - Notation When randomly selecting an adult, A...Ch. 4.2 - Notation When randomly selecting adults, let M...Ch. 4.2 - Sample for a Poll There are 15,524,971 adults in...Ch. 4.2 - Rule of Complements When randomly selecting an...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20; use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - Redundancy. Exercises 25 and 26 involve...Ch. 4.2 - Redundancy. Exercises 25 and 26 involve...Ch. 4.2 - Acceptance Sampling. With one method of a...Ch. 4.2 - Acceptance Sampling. With one method of a...Ch. 4.2 - In Exercises 29 and 30, find the probabilities and...Ch. 4.2 - Prob. 30BSCCh. 4.2 - Surge Protectors Refer to the accompanying figure...Ch. 4.2 - Prob. 32BBCh. 4.2 - Exclusive Or The exclusive or means either one or...Ch. 4.2 - Complements and the Addition Rule Refer to the...Ch. 4.3 - Language: Complement of At Least One Let A = the...Ch. 4.3 - Probability of At Least One Let A = the event of...Ch. 4.3 - Notation When selecting one of your Facebook...Ch. 4.3 - Notation When selecting one of your Facebook...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Probability of a Girl Assuming that boys and girls...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - Redundancy in Computer Hard Drives Assume that...Ch. 4.3 - Redundancy in Stadium Generators Large stadiums...Ch. 4.3 - Composite Drug Test Based on the data in Table 4-1...Ch. 4.3 - Composite Water Samples The Fairfield County...Ch. 4.3 - Shared Birthdays Find the probability that of 25...Ch. 4.4 - Notation What does the symbol ! represent? Six...Ch. 4.4 - New Jersey Pick 6 In the New Jersey Pick 6 lottery...Ch. 4.4 - Oregon Pick 4 In the Oregon Pick 4 lottery game, a...Ch. 4.4 - Combination Lock The typical combination lock uses...Ch. 4.4 - In Exercises 536, express all probabilities as...Ch. 4.4 - Social Security Numbers A Social Security number...Ch. 4.4 - Quinela In a horse race, a quinela bet is won if...Ch. 4.4 - Soccer Shootout In soccer, a tie at the end of...Ch. 4.4 - Grading Exams Your professor has just collected...Ch. 4.4 - Radio Station Call Letters If radio station call...Ch. 4.4 - Scheduling Routes A presidential candidate plans...Ch. 4.4 - Survey Reliability A survey with 12 questions is...Ch. 4.4 - Safety with Numbers The author owns a safe in...Ch. 4.4 - Electricity When testing for current in a cable...Ch. 4.4 - Sorting Hat At Hogwarts School of Witchcraft and...Ch. 4.4 - Moving Company The United Van Lines moving company...Ch. 4.4 - Powerball As of this writing, the Powerball...Ch. 4.4 - Teed Off When four golfers are about to begin a...Ch. 4.4 - ZIP Code If you randomly select five digits, each...Ch. 4.4 - FedEx Deliveries With a short time remaining in...Ch. 4.4 - Phone Numbers Current rules for telephone area...Ch. 4.4 - Classic Counting Problem A classic counting...Ch. 4.4 - Corporate Officers and Committees The Digital Pet...Ch. 4.4 - ATM You want to obtain cash by using an ATM, but...Ch. 4.4 - Party Mix DJ Marty T is hosting a party tonight...Ch. 4.4 - Identity Theft with Credit Cards Credit card...Ch. 4.4 - What a Word! One of the longest words in standard...Ch. 4.4 - Phase I of a Clinical Trial A clinical test on...Ch. 4.4 - Mega Millions As of this writing, the Mega...Ch. 4.4 - Designing Experiment Clinical trials of Nasonex...Ch. 4.4 - Morse Codes The International Morse code is a way...Ch. 4.4 - Mendels Peas Mendel conducted some his famous...Ch. 4.4 - Change for a Quarter How many different ways can...Ch. 4.4 - Counting with Fingers How many different ways can...Ch. 4.4 - Change for a Quarter How many different ways can...Ch. 4.4 - Win 1 Billion Quicken Loans offered a prize of 1...Ch. 4.4 - Computer Variable Names A common computer...Ch. 4.4 - High Fives a. Five mathletes celebrate after...Ch. 4 - Standard Tests Standard tests, such as the SAT or...Ch. 4 - Rain As the author is creating this exercise, a...Ch. 4 - Months If a month is randomly selected after...Ch. 4 - Social Networking Based on data from the Pew...Ch. 4 - Subjective Probability Estimate the probability...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - Prob. 10RECh. 4 - Black Cars Use subjective probability to estimate...Ch. 4 - Vision Correction About 75% of the U.S. population...Ch. 4 - National Statistics Day a. If a person is randomly...Ch. 4 - Composite Sampling for Diabetes Currently, the...Ch. 4 - Wild Card Lottery The Wild Card lottery is run in...Ch. 4 - Pennsylvania Cash 5 In the Pennsylvania Cash 5...Ch. 4 - Redundancy Using Braun battery-powered alarm...Ch. 4 - Exacta In a horse race, an exacta bet is won by...Ch. 4 - Fatal Drunk Driving Listed below are the blood...Ch. 4 - Fatal Drunk Driving Use the same data given in...Ch. 4 - Organ Donors USA Today provided information about...Ch. 4 - Sampling Eye Color Based on a study by Dr. P....Ch. 4 - Prob. 5CRECh. 4 - New Lottery Game In the Monopoly Millionaires Club...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...
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