Statistics for Business & Economics, Revised (MindTap Course List)
12th Edition
ISBN: 9781285846323
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: South-Western College Pub
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Textbook Question
Chapter 7.5, Problem 18E
A population has a
- a. What is the
expected value of - b. What is the standard deviation of
- c. Show the sampling distribution of
- d. What does the sampling distribution of
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Throughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2.
1. Show that
AAB (ANB) U (BA) = (AUB) (AB),
Α' Δ Β = Α Δ Β,
{A₁ U A2} A {B₁ U B2) C (A1 A B₁}U{A2 A B2).
16. Show that, if X and Y are independent random variables, such that E|X|< ∞,
and B is an arbitrary Borel set, then
EXI{Y B} = EX P(YE B).
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
Chapter 7 Solutions
Statistics for Business & Economics, Revised (MindTap Course List)
Ch. 7.2 - Consider a finite population with five elements...Ch. 7.2 - Assume a finite population has 350 elements. Using...Ch. 7.2 - Fortune publishes data on sales, profits, assets,...Ch. 7.2 - The 10 most active stocks on the New York Stock...Ch. 7.2 - A student government organization is interested in...Ch. 7.2 - The County and City Data Book, published by the...Ch. 7.2 - Assume that we want to identify a simple random...Ch. 7.2 - The following stocks make up the Dow Jones...Ch. 7.2 - The Wall Street Journal provides the net asset...Ch. 7.2 - Indicate which of the following situations involve...
Ch. 7.3 - The following data are from a simple random...Ch. 7.3 - A survey question for a sample of 150 individuals...Ch. 7.3 - A sample of 5 months of sales data provided the...Ch. 7.3 - BusinessWeek published information on 283 equity...Ch. 7.3 - Many drugs used to treat cancer are expensive....Ch. 7.3 - A sample of 426 U.S. adults age 50 and older were...Ch. 7.3 - The American Association of Individual Investors...Ch. 7.5 - A population has a mean of 200 and a standard...Ch. 7.5 - A population has a mean of 200 and a standard...Ch. 7.5 - Assume the population standard deviation is = 25....Ch. 7.5 - Suppose a random sample of size 50 is selected...Ch. 7.5 - Refer to the EAI sampling problem. Suppose a...Ch. 7.5 - In the EAI sampling problem (see Figure 7.5), we...Ch. 7.5 - Barrons reported that the average number of weeks...Ch. 7.5 - The College Board reported the following mean...Ch. 7.5 - The mean annual cost of automobile insurance is...Ch. 7.5 - The Economic Policy Institute periodically issues...Ch. 7.5 - The average score for male golfers is 95 and the...Ch. 7.5 - The mean preparation fee HR Block charged retail...Ch. 7.5 - To estimate the mean age for a population of 4000...Ch. 7.6 - A sample of size 100 is selected from a population...Ch. 7.6 - A population proportion is .40. A sample of size...Ch. 7.6 - Assume that the population proportion is .55....Ch. 7.6 - The population proportion is .30. What is the...Ch. 7.6 - The president of Doerman Distributors, Inc.,...Ch. 7.6 - The Wall Street Journal reported that the age at...Ch. 7.6 - People end up tossing 12% of what they buy at the...Ch. 7.6 - Forty-two percent of primary care doctors think...Ch. 7.6 - In 2008 the Better Business Bureau settled 75% of...Ch. 7.6 - The Grocery Manufacturers of America reported that...Ch. 7.6 - The Food Marketing Institute shows that 17% of...Ch. 7 - U.S. News World Report publishes comprehensive...Ch. 7 - The latest available data showed health...Ch. 7 - Foot Locker uses sales per square foot as a...Ch. 7 - The mean television viewing time for Americans is...Ch. 7 - After deducting grants based on need, the average...Ch. 7 - Three firms carry inventories that differ in size....Ch. 7 - A researcher reports survey results by stating...Ch. 7 - A production process is checked periodically by a...Ch. 7 - About 28% of private companies are owned by women...Ch. 7 - A market research firm conducts telephone surveys...Ch. 7 - Advertisers contract with Internet service...Ch. 7 - The proportion of individuals insured by the...Ch. 7 - Lori Jeffrey is a successful sales representative...
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- Exercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and B, and A and B.arrow_forward8. Show that, if {Xn, n ≥ 1) are independent random variables, then sup X A) < ∞ for some A.arrow_forward8- 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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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