STATS:DATA+MODELS-W/DVD
4th Edition
ISBN: 9780321986498
Author: DeVeaux
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 2.2, Problem 7JC
To determine
Explain whether the eye colour and gender are independent.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
30 Explain how you can use the empirical rule
to find out whether a data set is mound-
shaped, using only the values of the data
themselves (no histogram available).
5. Let X be a positive random variable with finite variance, and let A = (0, 1).
Prove that
P(X AEX) 2 (1-A)² (EX)²
EX2
6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows:
P(X=-x) = P(X = x)=p. P(X=0)= 1-2p.
Show that there is equality in Chebyshev's inequality for X.
This means that Chebyshev's inequality, in spite of being rather crude, cannot be
improved without additional assumptions.
Chapter 2 Solutions
STATS:DATA+MODELS-W/DVD
Ch. 2.2 - A statistics class reports the following data on...Ch. 2.2 - Prob. 2JCCh. 2.2 - Prob. 3JCCh. 2.2 - Prob. 4JCCh. 2.2 - Prob. 5JCCh. 2.2 - Prob. 6JCCh. 2.2 - Prob. 7JCCh. 2 - Prob. 1ECh. 2 - Nonoccupant fatalities The frequencies of traffic...Ch. 2 - Movie genres The Motion Picture Association of...
Ch. 2 - 6. Marriage in decline Changing attitudes about...Ch. 2 - 5. Movies again The following table summarizes 348...Ch. 2 - 6. Labor force The following table shows the labor...Ch. 2 - 11. Movie genres II The pie chart summarizes the...Ch. 2 - Movie ratings The pie chart shows the ratings...Ch. 2 - 13. Genres again Here is a bar chart summarizing...Ch. 2 - Ratings again Here is a bar chart of the movie...Ch. 2 - 37. Magnet schools An article in the Winter 2003...Ch. 2 - 38. Magnet schools again The Chance article about...Ch. 2 - Causes of death 2011 The Centers for Disease...Ch. 2 - Plane crashes An investigation compiled...Ch. 2 - Oil spills 2013 Data from the International Tanker...Ch. 2 - 20. Winter Olympics 2010 Twenty-six countries won...Ch. 2 - 21. Global warming The Pew Research Center for the...Ch. 2 - 44. Modalities A survey of athletic trainers asked...Ch. 2 - 23. Teen smokers The organization Monitoring the...Ch. 2 - 26. Handguns In an effort to reduce the number of...Ch. 2 - 25. Movies by genre and rating Here’s a table that...Ch. 2 - 26. The last picture show Here’s another table...Ch. 2 - 29. Seniors Prior to graduation, a high school...Ch. 2 - 30. Politics Students in an Intro Stats course...Ch. 2 - Prob. 29ECh. 2 - 34. Politics revisited Look again at the table of...Ch. 2 - Prob. 31ECh. 2 - 36. More politics Look once more at the table...Ch. 2 - 37. Back to school Examine the table about...Ch. 2 - 38. Parking lots A survey of autos parked in...Ch. 2 - Prob. 35ECh. 2 - 40. Twin births In 2000, the Journal of the...Ch. 2 - Prob. 37ECh. 2 - 42. Obesity and exercise The Centers for Disease...Ch. 2 - 43. Anorexia Hearing anecdotal reports that some...Ch. 2 - Prob. 40ECh. 2 - 41. Drivers’ licenses 2011 The table on the next...Ch. 2 - 46. Tattoos A study by the University of Texas...Ch. 2 - Prob. 43ECh. 2 - 50. Delivery service A company must decide which...Ch. 2 - 51. Graduate admissions A 1975 article in the...Ch. 2 - 52. Be a Simpson Can you design a Simpson’s...
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
- 4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined as a product of independent, identically distributed random variables with mean 1 (under the so-called null hypothesis), and the, sometimes more convenient, log-likelihood, log L, which was a sum of independent, identically distributed random variables, which, however, do not have mean log 1 = 0. (a) Verify that the last claim is correct, by proving the more general statement, namely that, if Y is a non-negative random variable with finite mean, then E(log Y) log(EY). (b) Prove that, in fact, there is strict inequality: E(log Y) < log(EY), unless Y is degenerate. (c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a glimpse on (b).arrow_forward3. Prove that, for any random variable X, the minimum of E(X - a)² is attained for a = EX. Provedarrow_forward
- 7. Cantelli's inequality. Let X be a random variable with finite variance, o². (a) Prove that, for x ≥ 0, P(X EX2x)≤ 02 x² +0² 202 P(|X - EX2x)<≤ (b) Find X assuming two values where there is equality. (c) When is Cantelli's inequality better than Chebyshev's inequality? (d) Use Cantelli's inequality to show that med (X) - EX ≤ o√√3; recall, from Proposition 6.1, that an application of Chebyshev's inequality yields the bound o√√2. (e) Generalize Cantelli's inequality to moments of order r 1.arrow_forwardThe college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forwardThe Honolulu Advertiser stated that in Honolulu there was an average of 659 burglaries per 400,000 households in a given year. In the Kohola Drive neighborhood there are 321 homes. Let r be the number of homes that will be burglarized in a year. Use the formula for Poisson distribution. What is the value of p, the probability of success, to four decimal places?arrow_forward
- The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forwardWhat was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Use a histogram and graph the probability distribution. Using the graph of the probability distribution determine the probability that a British nurse selected at random in 1851 would be 40 years of age or older. Round your answer to nearest thousandth. Age range (yr) 20–29 30–39 40–49 50–59 60–69 70–79 80+ Midpoint (x) 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%arrow_forwardWhat was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Use a histogram and graph the probability distribution. Using the graph of the probability distribution determine the probability that a British nurse selected at random in 1851 would be 40 years of age or older. Round your answer to nearest thousandth. Age range (yr) 20–29 30–39 40–49 50–59 60–69 70–79 80+ Midpoint (x) 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%arrow_forward
- There are 4 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. Make a histogram for the probability distribution.arrow_forwardshow all stepsarrow_forwardMost people know that the probability of getting a head when you flip a fair coin is . You want to use the relative frequency of the event to show that the probability is . How many times should you simulate flipping the coin in the experiment? Would it be better to use 300 trials or 3000 trials? Explain.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License