EBK STATISTICS FOR ENGINEERS AND SCIENT
4th Edition
ISBN: 9780100274389
Author: Navidi
Publisher: YUZU
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Chapter 4, Problem 10SE
a.
To determine
Check whether it is possible to compute the
b.
To determine
Check whether it is possible to compute the probability that the stiffness of a randomly chosen beam is greater than 32.2 k N/mm in a sample of 100 beams. If so compute the probability. If not explain the reason.
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The class will include a data exercise where students will be introduced to publicly available data sources. Students will gain experience in manipulating data from the web and applying it to understanding the economic and demographic conditions of regions in the U.S. Regions and topics of focus will be determined (by the student with instructor approval) prior to April. What data exercise can I do to fulfill this requirement? Please explain.
Consider the ceocomp dataset of compensation information for the CEO’s of 100 U.S. companies. We wish to fit aregression model to assess the relationship between CEO compensation in thousands of dollars (includes salary andbonus, but not stock gains) and the following variates:AGE: The CEOs age, in yearsEDUCATN: The CEO’s education level (1 = no college degree; 2 = college/undergrad. degree; 3 = grad. degree)BACKGRD: Background type(1= banking/financial; 2 = sales/marketing; 3 = technical; 4 = legal; 5 = other)TENURE: Number of years employed by the firmEXPER: Number of years as the firm CEOSALES: Sales revenues, in millions of dollarsVAL: Market value of the CEO's stock, in natural logarithm unitsPCNTOWN: Percentage of firm's market value owned by the CEOPROF: Profits of the firm, before taxes, in millions of dollars1) Create a scatterplot matrix for this dataset. Briefly comment on the observed relationships between compensationand the other variates.Note that companies with negative…
6 (Model Selection, Estimation and Prediction of GARCH) Consider the daily returns rt
of General Electric Company stock (ticker: "GE") from "2021-01-01" to "2024-03-31",
comprising a total of 813 daily returns. Using the "fGarch" package of R, outputs of
fitting three GARCH models to the returns are given at the end of this question.
Model 1 ARCH (1) with standard normal innovations;
Model 2
Model 3
GARCH (1, 1) with Student-t innovations;
GARCH (2, 2) with Student-t innovations;
Based on the outputs, answer the following questions.
(a) What can be inferred from the Standardized Residual Tests conducted on Model 1?
(b) Which model do you recommend for prediction between Model 2 and Model 3?
Why?
(c) Write down the fitted model for the model that you recommended in Part (b).
(d) Using the model recommended in Part (b), predict the conditional volatility in the
next trading day, specifically trading day 814.
Chapter 4 Solutions
EBK STATISTICS FOR ENGINEERS AND SCIENT
Ch. 4.1 - After scoring a touchdown, a football team may...Ch. 4.1 - A certain brand of dinnerware set comes in three...Ch. 4.1 - When a certain glaze is applied to a ceramic...Ch. 4.1 - Let X and Y be Bernoulli random variables. Let Z =...Ch. 4.1 - A penny and a nickel are tossed. Both are fair...Ch. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.2 - Let X Bin(7, 0.3). Find a. P(X = 1) b. P(X = 2)...Ch. 4.2 - Let X Bin(9, 0.4). Find a. P(X 6) b. P(X 2) c....Ch. 4.2 - Prob. 3E
Ch. 4.2 - At a certain airport, 75% of the flights arrive on...Ch. 4.2 - Of all the registered automobiles in a certain...Ch. 4.2 - A fair die is rolled 8 times. a. What is the...Ch. 4.2 - Of all the weld failures in a certain assembly,...Ch. 4.2 - A general contracting firm experiences cost...Ch. 4.2 - Several million lottery tickets are sold, and 60%...Ch. 4.2 - A quality engineer takes a random sample of 100...Ch. 4.2 - In a random sample of 100 parts ordered from...Ch. 4.2 - Of the items manufactured by a certain process,...Ch. 4.2 - Of the bolts manufactured for a certain...Ch. 4.2 - Gears produced by a grinding process are...Ch. 4.2 - A commuter must pass through three traffic lights...Ch. 4.2 - A distributor receives a large shipment of...Ch. 4.2 - A k out of n system is one in which there is a...Ch. 4.2 - Refer to Exercise 17 for the definition of a k out...Ch. 4.2 - A certain large shipment comes with a guarantee...Ch. 4.2 - An insurance company offers a discount to...Ch. 4.2 - A message consists of a string of bits (0s and...Ch. 4.2 - Let X Bin(n, p), and let Y = n X. Show that Y ...Ch. 4.2 - Porcelain figurines are sold for 10 if flawless,...Ch. 4.2 - Prob. 24ECh. 4.2 - (Requires material from Section 3.3.) Refer to...Ch. 4.2 - If p is a success probability, the quantity p/(1 ...Ch. 4.3 - Let X Poisson(4). Find a. P(X = 1) b. P(X = 0) c....Ch. 4.3 - The number of flaws in a given area of aluminum...Ch. 4.3 - In a certain city, the number of potholes on a...Ch. 4.3 - Geologists estimate the time since the most recent...Ch. 4.3 - Prob. 5ECh. 4.3 - One out of every 5000 individuals in a population...Ch. 4.3 - The number of hits on a certain website follows a...Ch. 4.3 - The number of cars arriving at a given...Ch. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - A microbiologist wants to estimate the...Ch. 4.3 - Two-dimensional Poisson process. The number of...Ch. 4.3 - The number of defective components produced by a...Ch. 4.3 - The probability that a certain radioactive mass...Ch. 4.3 - The number of flaws in a certain type of lumber...Ch. 4.3 - Grandma is trying out a new recipe for raisin...Ch. 4.3 - Mom and Grandma are each baking chocolate chip...Ch. 4.3 - Prob. 18ECh. 4.3 - Someone claims that a certain suspension contains...Ch. 4.3 - A physicist wants to estimate the rate of...Ch. 4.3 - Prob. 21ECh. 4.4 - Twenty air-conditioning units have been brought in...Ch. 4.4 - There are 30 restaurants in a certain town. Assume...Ch. 4.4 - The probability that a computer running a certain...Ch. 4.4 - A traffic light at a certain intersection is green...Ch. 4.4 - Refer to Exercise 4. Let Y denote the number of...Ch. 4.4 - Refer to Exercise 4. What is the probability that...Ch. 4.4 - If X Geom(p), what is the most probable value of...Ch. 4.4 - A process that fills packages is stopped whenever...Ch. 4.4 - A system is tested for faults once per hour. If...Ch. 4.4 - Prob. 10ECh. 4.4 - In a lot of 10 microcircuits, 3 are defective....Ch. 4.4 - A lot of parts contains 500 items, 100 of which...Ch. 4.4 - Ten items are to be sampled from a lot of 60. If...Ch. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - A thermocouple placed in a certain medium produces...Ch. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.5 - Find the area under the normal curve a. To the...Ch. 4.5 - Find the area under the normal curve a. To the...Ch. 4.5 - Let Z N(0, 1). Find a constant c for which a. P(Z...Ch. 4.5 - If X N(2, 9), compute a. P(X 2) b. P(1 X 7) c....Ch. 4.5 - The lifetime of a battery in a certain application...Ch. 4.5 - The temperature recorded by a certain thermometer...Ch. 4.5 - Scores on a standardized test are approximately...Ch. 4.5 - Weights of female cats of a certain breed are...Ch. 4.5 - The lifetime of a lightbulb in a certain...Ch. 4.5 - In a certain university, math SAT scores for the...Ch. 4.5 - Penicillin is produced by the Penicillium fungus,...Ch. 4.5 - Specifications for an aircraft bolt require that...Ch. 4.5 - A cylindrical hole is drilled in a block, and a...Ch. 4.5 - Shafts manufactured for use in optical storage...Ch. 4.5 - The fill volume of cans filled by a certain...Ch. 4.5 - The amount of paint required to paint a surface...Ch. 4.5 - A fiber-spinning process currently produces a...Ch. 4.5 - The area covered by 1 L of a certain stain is...Ch. 4.5 - Prob. 19ECh. 4.5 - The quality-assurance program for a certain...Ch. 4.5 - Two resistors, with resistances R1 and R2, are...Ch. 4.5 - The molarity of a solute in solution is defined to...Ch. 4.5 - A binary message m, where m is equal either to 0...Ch. 4.5 - Refer to Exercise 23. Assume that if m = 0, the...Ch. 4.5 - A company receives a large shipment of bolts. The...Ch. 4.5 - Prob. 26ECh. 4.6 - The lifetime (in days) of a certain electronic...Ch. 4.6 - The article Assessment of Dermopharmacokinetic...Ch. 4.6 - The body mass index (BMI) of a person is defined...Ch. 4.6 - The article Stochastic Estimates of Exposure and...Ch. 4.6 - If a resistor with resistance R ohms carries a...Ch. 4.6 - Refer to Exercise 5. Suppose 10 circuits are...Ch. 4.6 - The article Withdrawal Strength of Threaded Nails...Ch. 4.6 - Choose the best answer, and explain. If X is a...Ch. 4.6 - Prob. 9ECh. 4.6 - A manufacturer claims that the tensile strength of...Ch. 4.6 - Let X1,...., Xn be independent lognormal random...Ch. 4.7 - Let T Exp(0.45). Find a. T b. T2 c. P(T 3) d....Ch. 4.7 - The time between requests to a web server is...Ch. 4.7 - A catalyst researcher states that the diameters,...Ch. 4.7 - The distance between flaws on a long cable is...Ch. 4.7 - Refer to Exercise 3. Suppose that the diameters of...Ch. 4.7 - Someone claims that the waiting time, in minutes,...Ch. 4.7 - A certain type of component can be purchased new...Ch. 4.7 - A radioactive mass emits particles according to a...Ch. 4.7 - The number of traffic accidents at a certain...Ch. 4.7 - The distance between consecutive flaws on a roll...Ch. 4.7 - A light fixture contains five lightbulbs. The...Ch. 4.8 - Prob. 1ECh. 4.8 - Resistors are labeled 100 . In fact, the actual...Ch. 4.8 - Let T (4,0.5). a.Find T. b.Find T. c.Find P(T ...Ch. 4.8 - Prob. 4ECh. 4.8 - Prob. 5ECh. 4.8 - The lifetime, in years, of a type of small...Ch. 4.8 - Let T Weibull (0.5, 3). a.Find T. b.Find T....Ch. 4.8 - Prob. 8ECh. 4.8 - Prob. 9ECh. 4.8 - The lifetime of a certain battery is modeled with...Ch. 4.8 - The lifetime of a cooling fan, in hours, that is...Ch. 4.8 - Someone suggests that the lifetime T (in days) of...Ch. 4.8 - A system consists of two components connected in...Ch. 4.8 - Prob. 14ECh. 4.8 - Prob. 15ECh. 4.8 - Prob. 16ECh. 4.8 - Prob. 17ECh. 4.9 - Choose the best answer to fill in the blank. If an...Ch. 4.9 - Choose the best answer to fill in the blank. The...Ch. 4.9 - Let X1 and X2 be independent, each with unknown...Ch. 4.9 - Let X1,, Xn be a simple random sample from a N(,2)...Ch. 4.9 - Let X Geom (p). Find the MLE of p.Ch. 4.9 - Let X1, Xn be a random sample from a population...Ch. 4.9 - Maximum likelihood estimates possess the property...Ch. 4.9 - Let X1,, Xn be a random sample from a N(, 1)...Ch. 4.9 - Let X1, Xn be a random sample from a N(0,2)...Ch. 4.9 - Let X1,, Xn be a random sample from a N(,2)...Ch. 4.10 - Prob. 1ECh. 4.10 - As part of a quality-control study aimed at...Ch. 4.10 - Below are the durations (in minutes) of 40...Ch. 4.10 - Prob. 4ECh. 4.10 - Construct a normal probability plot for the PM...Ch. 4.10 - Construct a normal probability plot for the logs...Ch. 4.10 - Can the plot in Exercise 6 be used to determine...Ch. 4.10 - In the article Assessment of...Ch. 4.11 - Bottles filled by a certain machine are supposed...Ch. 4.11 - A 500-page book contains 250 sheets of paper. The...Ch. 4.11 - A commuter encounters four traffic lights each day...Ch. 4.11 - Among all the income-tax forms filed in a certain...Ch. 4.11 - Bags checked for a certain airline flight have a...Ch. 4.11 - The amount of warpage in a type of wafer used in...Ch. 4.11 - The time spent by a customer at a checkout counter...Ch. 4.11 - Drums labeled 30 L are filled with a solution from...Ch. 4.11 - The temperature of a solution will be estimated by...Ch. 4.11 - Among the adults in a large city, 30% have a...Ch. 4.11 - In a process that manufactures bearings, 90% of...Ch. 4.11 - A machine produces 1000 steel O-rings per day....Ch. 4.11 - Radioactive mass A emits particles at a mean rate...Ch. 4.11 - The concentration of particles in a suspension is...Ch. 4.11 - The concentration of particles in a suspension is...Ch. 4.11 - A battery manufacturer claims that the lifetime of...Ch. 4.11 - A new process has been designed to make ceramic...Ch. 4.11 - The manufacture of a certain part requires two...Ch. 4.11 - Seventy percent of rivets from vendor A meet a...Ch. 4.11 - Radiocarbon dating: Carbon-14 is a radioactive...Ch. 4 - An airplane has 100 seats for passengers. Assume...Ch. 4 - The number of large cracks in a length of pavement...Ch. 4 - Pea plants contain two genes for seed color, each...Ch. 4 - A simple random sample X1,,Xn is drawn from a...Ch. 4 - The Environmental Protection Agency (EPA) has...Ch. 4 - In the article Occurrence and Distribution of...Ch. 4 - Medication used to treat a certain condition is...Ch. 4 - A certain type of plywood consists of five layers....Ch. 4 - Prob. 9SECh. 4 - Prob. 10SECh. 4 - In a certain process, the probability of producing...Ch. 4 - A process that polishes a mirrored surface leaves...Ch. 4 - Prob. 13SECh. 4 - Prob. 14SECh. 4 - Thicknesses of shims are normally distributed with...Ch. 4 - The lifetime of a microprocessor is exponentially...Ch. 4 - Prob. 17SECh. 4 - Prob. 18SECh. 4 - A cereal manufacturer claims that the gross weight...Ch. 4 - Prob. 20SECh. 4 - Prob. 21SECh. 4 - Prob. 22SECh. 4 - Prob. 23SECh. 4 - Prob. 24SECh. 4 - Let X Geom(p). Let s 0 be an integer. a.Show...Ch. 4 - Prob. 26SECh. 4 - Prob. 27SECh. 4 - Prob. 28SECh. 4 - Prob. 29SECh. 4 - Prob. 30SE
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