Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
6th Edition
ISBN: 9781337115186
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Chapter 3.1, Problem 4E
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Proposition 1.1 Suppose that X1, X2,... are random variables. The following
quantities are random variables:
(a) max{X1, X2) and min(X1, X2);
(b) sup, Xn and inf, Xn;
(c) lim sup∞ X
and lim inf∞ Xn-
(d) If Xn(w) converges for (almost) every w as n→ ∞, then lim-
random variable.
→ Xn is a
Exercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and
B, and A and B.
8. Show that, if {Xn, n ≥ 1) are independent random variables, then
sup X A) < ∞ for some A.
Chapter 3 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Ch. 3.1 - 1. Consider a sample with data values of 10, 20,...Ch. 3.1 - 2. Consider a sample with data values of 10, 20,...Ch. 3.1 - 3. Consider the following data and corresponding...Ch. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - 7. The average number of minutes Americans commute...Ch. 3.1 - Middle-Level Manager Salaries. Suppose that an...Ch. 3.1 - 9. Which companies spend the most money on...Ch. 3.1 - Advertising Spending. Which companies spend the...
Ch. 3.1 - Prob. 11ECh. 3.1 -
The Big Bang Theory, a situation comedy...Ch. 3.1 - Automobile Fuel Efficiencies. In automobile...Ch. 3.1 -
The data contained in the DATAfile named...Ch. 3.1 - 15. Martinez Auto Supplies has retail stores...Ch. 3.1 - 16. The grade point average for college students...Ch. 3.1 - 17. The following table shows the total return and...Ch. 3.1 - 18. Based on a survey of master’s programs in...Ch. 3.1 - Annual revenue for Corning Supplies grew by 5.5%...Ch. 3.1 - Suppose that at the beginning of Year 1 you...Ch. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.2 - 23. Consider a sample with data values of 10, 20,...Ch. 3.2 - Prob. 24ECh. 3.2 - Consider a sample with data values of 27, 25, 20,...Ch. 3.2 - Price of Unleaded Gasoline. Data collected by the...Ch. 3.2 - Round-Trip Flight Prices. The following table...Ch. 3.2 -
The Australian Open is the first of the four...Ch. 3.2 - Air Quality Index. The Los Angeles Times regularly...Ch. 3.2 - Prob. 30ECh. 3.2 -
The results of Accounting Principals’ latest...Ch. 3.2 - Advertising Spend by Companies. Advertising Age...Ch. 3.2 - Scores turned in by an amateur golfer at the...Ch. 3.2 - Consistency of Running Times. The following times...Ch. 3.3 - 35. Consider a sample with data values of 10, 20,...Ch. 3.3 - 36. Consider a sample with a mean of 500 and a...Ch. 3.3 - 37. Consider a sample with a mean of 30 and a...Ch. 3.3 - 38. Suppose the data have a bell-shaped...Ch. 3.3 - 39. The results of a national survey showed that...Ch. 3.3 - 40. The energy information Administration reported...Ch. 3.3 - 41. The Graduate Management Admission Test (GMAT)...Ch. 3.3 - 42. Many families in California are using backyard...Ch. 3.3 -
According to a Los Angeles Times study of more...Ch. 3.3 - NCAA Basketball Game Scores. A sample of 10 NCAA...Ch. 3.3 -
The Wall Street Journal reported that Walmart...Ch. 3.4 - Consider a sample with data values of 27, 25, 20,...Ch. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Naples Half-Marathon Times. Naples, Florida, hosts...Ch. 3.4 - Pharmaceutical Company Sales. Annual sales, in...Ch. 3.4 - Cell Phone Companies Customer Satisfaction....Ch. 3.4 - Most Admired Companies. Fortune magazine’s list of...Ch. 3.4 - Prob. 54ECh. 3.5 - Five observations taken for two variables...Ch. 3.5 - Prob. 56ECh. 3.5 - The DATAfile TwoStocks contains adjusted monthly...Ch. 3.5 - Driving Speed and Fuel Efficiency. A department of...Ch. 3.5 - Smoke Detector Use and Death Rates. Over the past...Ch. 3.5 - Stock Market Indexes Comparison. The Russell 1000...Ch. 3.5 - Best Private Colleges. A random sample of 30...Ch. 3 - Americans Dining Out. Americans tend to dine out...Ch. 3 - NCAA Football Coaches Salaries. A 2017 USA Today...Ch. 3 - Physician Office Waiting Times. The average...Ch. 3 - Worker Productivity and Insomnia. U.S. companies...Ch. 3 -
A study of smartphone users shows that 68% of...Ch. 3 - Work Commuting Methods. Public transportation and...Ch. 3 - Household Incomes. The following data represent a...Ch. 3 - Restaurant Chains’ Sales per Store. The data...Ch. 3 - Prob. 70SECh. 3 - NFL Teams Worth. In 2014, the 32 teams in the...Ch. 3 - MLB Team Winning Percentages. Does a major league...Ch. 3 - 73. The days to maturity for a sample of five...Ch. 3 - 74. Automobiles traveling on a road with a posted...Ch. 3 - Annual Returns for Panama Railroad Company Stock....Ch. 3 - Pelican Stores, a division of National Clothing,...Ch. 3 -
The motion picture industry is a competitive...Ch. 3 - The pursuit of a higher education degree in...Ch. 3 - Although millions of elephants once roamed across...
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- 8- 6. Show that, for any random variable, X, and a > 0, 8 心 P(xarrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that 00 (P(X ≤ x ≤ Y) - P(X ≤ x ≤ X))dx = E Y — E X.arrow_forward(b) Define a simple random variable. Provide an example.arrow_forward17. (a) Define the distribution of a random variable X. (b) Define the distribution function of a random variable X. (c) State the properties of a distribution function. (d) Explain the difference between the distribution and the distribution function of X.arrow_forward16. (a) Show that IA(w) is a random variable if and only if A E Farrow_forward15. Let 2 {1, 2,..., 6} and Fo({1, 2, 3, 4), (3, 4, 5, 6}). (a) Is the function X (w) = 21(3, 4) (w)+711.2,5,6) (w) a random variable? Explain. (b) Provide a function from 2 to R that is not a random variable with respect to (N, F). (c) Write the distribution of X. (d) Write and plot the distribution function of X.arrow_forward20. Define the o-field R2. Explain its relation to the o-field R.arrow_forward7. Show that An → A as n→∞ I{An} - → I{A} as n→ ∞.arrow_forward7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).arrow_forward19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.arrow_forward18. Define a bivariate random variable. Provide an example.arrow_forward6. (a) Let (, F, P) be a probability space. Explain when a subset of ?? is measurable and why. (b) Define a probability measure. (c) Using the probability axioms, show that if AC B, then P(A) < P(B). (d) Show that P(AUB) + P(A) + P(B) in general. Write down and prove the formula for the probability of the union of two sets.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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