An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 4.18, Problem 19E
a.
To determine
Check whether the events A and B are independent or not.
b.
To determine
Check whether the events A and C are independent or not.
c.
To determine
Check whether the events B and C are independent or not.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c
Overhead Costs Billable Hours345000 3000385000 4000410000 5000462000 6000530000 7000545000 8000
Using the accompanying Home Market Value data and associated regression line,
Market ValueMarket Valueequals=$28,416plus+$37.066×Square
Feet, compute the errors associated with each observation using the formula
e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi
and construct a frequency distribution and histogram.
Square Feet Market Value1813 911001916 1043001842 934001814 909001836 1020002030 1085001731 877001852 960001793 893001665 884001852 1009001619 967001690 876002370 1139002373 1131001666 875002122 1161001619 946001729 863001667 871001522 833001484 798001589 814001600 871001484 825001483 787001522 877001703 942001485 820001468 881001519 882001518 885001483 765001522 844001668 909001587 810001782 912001483 812001519 1007001522 872001684 966001581 86200
a. Find the value of A.b. Find pX(x) and py(y).c. Find pX|y(x|y) and py|X(y|x)d. Are x and y independent? Why or why not?
Chapter 4 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 4.18 - Indicate which interpretation of the probability...Ch. 4.18 - If you are having a stroke, it is critical that...Ch. 4.18 - In reporting highway safety, the National Highway...Ch. 4.18 - In a cable TV program concerning the risk of...Ch. 4.18 - The gaming commission in its annual examination of...Ch. 4.18 - The state vehicle inspection bureau provided the...Ch. 4.18 - The Texas Lottery has a game, Daily 4, in which a...Ch. 4.18 - A die is rolled two times. Provide a list of the...Ch. 4.18 - Refer to Exercise 4.10. Assume that the die is a...Ch. 4.18 - Refer to Exercise 4.11. a. Describe the event that...
Ch. 4.18 - Refer to Exercise 4.11. a. Are events A and B...Ch. 4.18 - A credit union takes a sample of four mortgages...Ch. 4.18 - A nuclear power plant has double redundancy on the...Ch. 4.18 - The population distribution in the United States...Ch. 4.18 - The makers of the candy MMs report that their...Ch. 4.18 - Refer to Exercise 4.11. Compute the following...Ch. 4.18 - Prob. 19ECh. 4.18 - Prob. 20ECh. 4.18 - Refer to Exercise 4.16. Let W be the event that...Ch. 4.18 - Is it possible for events A and B to be both...Ch. 4.18 - A survey of 1,000 U.S. government employees who...Ch. 4.18 - Refer to Exercise 4.23. Define the following...Ch. 4.18 - Prob. 25ECh. 4.18 - A large corporation has spent considerable time...Ch. 4.18 - The utility company in a large metropolitan area...Ch. 4.18 - Prob. 28ECh. 4.18 - Of a finance companys loans, 1% are defaulted (not...Ch. 4.18 - Refer to Exercise 4.29. Show that the posterior...Ch. 4.18 - Prob. 31ECh. 4.18 - In Example 4.4, compute the probability that the...Ch. 4.18 - Prob. 33ECh. 4.18 - In a January 15, 1998, article, the New England...Ch. 4.18 - Prob. 35ECh. 4.18 - Classify each of the following random variables as...Ch. 4.18 - Prob. 37ECh. 4.18 - Texting while driving is a very dangerous...Ch. 4.18 - Prob. 39ECh. 4.18 - The numbers of cars failing an emissions test on...Ch. 4.18 - A traditional call center has a simple mission:...Ch. 4.18 - A biologist randomly selects 10 portions of water,...Ch. 4.18 - Examine the accompanying newspaper clipping. Does...Ch. 4.18 - A survey is conducted to estimate the percentage...Ch. 4.18 - In an attempt to decrease drunk driving, police...Ch. 4.18 - The quality control department examines all the...Ch. 4.18 - Prob. 47ECh. 4.18 - The CFO of a hospital is concerned about the risk...Ch. 4.18 - Suppose the random variable y has a Poisson...Ch. 4.18 - Customers arrive at a grocery store checkout at a...Ch. 4.18 - A firm is considering using the Internet to...Ch. 4.18 - Prob. 52ECh. 4.18 - Prob. 53ECh. 4.18 - Prob. 54ECh. 4.18 - Prob. 55ECh. 4.18 - Prob. 56ECh. 4.18 - Prob. 57ECh. 4.18 - Prob. 58ECh. 4.18 - Prob. 59ECh. 4.18 - Prob. 60ECh. 4.18 - In Exercises 4.57 through 4.63, let z be a random...Ch. 4.18 - Prob. 62ECh. 4.18 - Prob. 63ECh. 4.18 - Prob. 64ECh. 4.18 - Let y be a random variable having a normal...Ch. 4.18 - Suppose that y is a random variable having a...Ch. 4.18 - Suppose that z is a random variable having a...Ch. 4.18 - Prob. 68ECh. 4.18 - Records maintained by the office of budget in a...Ch. 4.18 - The College Boards, which are administered each...Ch. 4.18 - Monthly sales figures for a particular food...Ch. 4.18 - Refer to Exercise 4.70. An honor society wishes to...Ch. 4.18 - Prob. 73ECh. 4.18 - Prob. 74ECh. 4.18 - A psychologist is interested in studying women who...Ch. 4.18 - Prob. 76ECh. 4.18 - A random sample of 16 measurements is drawn from a...Ch. 4.18 - Prob. 78ECh. 4.18 - Psychomotor retardation scores for a particular...Ch. 4.18 - Federal resources have been tentatively approved...Ch. 4.18 - Refer to Exercise 4.80. What size facility should...Ch. 4.18 - Based on the 1990 census, the number of hours per...Ch. 4.18 - The level of a particular pollutant, nitrogen...Ch. 4.18 - Refer to Exercise 4.83. A company has a fleet of...Ch. 4.18 - The baggage limit for an airplane is set at 100...Ch. 4.18 - A patient visits her doctor with concerns about...Ch. 4.18 - Critical key-entry errors in the data processing...Ch. 4.18 - Prob. 88ECh. 4.18 - Let y be a binomial random variable with n = 10...Ch. 4.18 - Prob. 90ECh. 4.18 - A marketing research firm advises a new client...Ch. 4.18 - Prob. 92ECh. 4.18 - Suppose a population consists of the 10...Ch. 4.18 - The fracture toughness in concrete specimens is a...Ch. 4.18 - One way to audit expense accounts for a large...Ch. 4.18 - The breaking strengths for 1-foot-square samples...Ch. 4.18 - Refer to Exercise 4.96. Suppose that a new...Ch. 4.18 - Refer to Exercise 4.97. Suppose that the mean...Ch. 4.18 - Prob. 99SECh. 4.18 - Prob. 100SECh. 4.18 - Experts consider high serum cholesterol levels to...Ch. 4.18 - Prob. 102SECh. 4.18 - Prob. 103SECh. 4.18 - Prob. 104SECh. 4.18 - Prob. 105SECh. 4.18 - Prob. 106SECh. 4.18 - Refer to Exercise 4.106. Plot the sampling...Ch. 4.18 - Random samples of size 5, 20, and 80 are drawn...Ch. 4.18 - Prob. 109SECh. 4.18 - Suppose the probability that a major earthquake...Ch. 4.18 - Prob. 111SECh. 4.18 - Airlines overbook (sell more tickets than there...Ch. 4.18 - Prob. 113SECh. 4.18 - As part of a study to determine factors that may...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- The PDF of an amplitude X of a Gaussian signal x(t) is given by:arrow_forwardThe PDF of a random variable X is given by the equation in the picture.arrow_forwardFor a binary asymmetric channel with Py|X(0|1) = 0.1 and Py|X(1|0) = 0.2; PX(0) = 0.4 isthe probability of a bit of “0” being transmitted. X is the transmitted digit, and Y is the received digit.a. Find the values of Py(0) and Py(1).b. What is the probability that only 0s will be received for a sequence of 10 digits transmitted?c. What is the probability that 8 1s and 2 0s will be received for the same sequence of 10 digits?d. What is the probability that at least 5 0s will be received for the same sequence of 10 digits?arrow_forward
- V2 360 Step down + I₁ = I2 10KVA 120V 10KVA 1₂ = 360-120 or 2nd Ratio's V₂ m 120 Ratio= 360 √2 H I2 I, + I2 120arrow_forwardQ2. [20 points] An amplitude X of a Gaussian signal x(t) has a mean value of 2 and an RMS value of √(10), i.e. square root of 10. Determine the PDF of x(t).arrow_forwardIn a network with 12 links, one of the links has failed. The failed link is randomlylocated. An electrical engineer tests the links one by one until the failed link is found.a. What is the probability that the engineer will find the failed link in the first test?b. What is the probability that the engineer will find the failed link in five tests?Note: You should assume that for Part b, the five tests are done consecutively.arrow_forward
- Problem 3. Pricing a multi-stock option the Margrabe formula The purpose of this problem is to price a swap option in a 2-stock model, similarly as what we did in the example in the lectures. We consider a two-dimensional Brownian motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices are modeled by the following equations: dX = dY₁ = X₁ (rdt+ rdt+0₁dW!) (²)), Y₁ (rdt+dW+0zdW!"), with Xo xo and Yo =yo. This corresponds to the multi-stock model studied in class, but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure P is already the risk-neutral measure (Both stocks have rate of return r). We write σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to exchange one share of X for one share of Y. That is, the option has payoff F=(Yr-XT). (a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for the process Xt. Reminder before proceeding to question (b): Girsanov's theorem…arrow_forwardProblem 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 (b) Using the formulas obtained in (a), show that the process (WA) is actually a 2- dimensional standard Brownian motion (i.e. show that each component is normal, with mean 0, variance t, and that their…arrow_forwardThe scores of 8 students on the midterm exam and final exam were as follows. Student Midterm Final Anderson 98 89 Bailey 88 74 Cruz 87 97 DeSana 85 79 Erickson 85 94 Francis 83 71 Gray 74 98 Harris 70 91 Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary. Test statistic: rs =arrow_forward
- Business discussarrow_forwardBusiness discussarrow_forwardI just need to know why this is wrong below: What is the test statistic W? W=5 (incorrect) and What is the p-value of this test? (p-value < 0.001-- incorrect) Use the Wilcoxon signed rank test to test the hypothesis that the median number of pages in the statistics books in the library from which the sample was taken is 400. A sample of 12 statistics books have the following numbers of pages pages 127 217 486 132 397 297 396 327 292 256 358 272 What is the sum of the negative ranks (W-)? 75 What is the sum of the positive ranks (W+)? 5What type of test is this? two tailedWhat is the test statistic W? 5 These are the critical values for a 1-tailed Wilcoxon Signed Rank test for n=12 Alpha Level 0.001 0.005 0.01 0.025 0.05 0.1 0.2 Critical Value 75 70 68 64 60 56 50 What is the p-value for this test? p-value < 0.001arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License