Statistical Techniques in Business and Economics, 16th Edition
16th Edition
ISBN: 9780078020520
Author: Douglas A. Lind, William G Marchal, Samuel A. Wathen
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 1, Problem 22DE
Refer to the Buena School District bus data, which report information on the school district’s bus fleet.
- a. Which of the variables are qualitative and which are quantitative?
- b. Determine the level of measurement for each variable.
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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 1 Solutions
Statistical Techniques in Business and Economics, 16th Edition
Ch. 1 - The Atlanta-based advertising firm Brandon and...Ch. 1 - What is the level of measurement reflected by the...Ch. 1 - What is the level of measurement for each of the...Ch. 1 - The San Francisco Chronicle is a large newspaper...Ch. 1 - For each of the following, determine whether the...Ch. 1 - Explain the difference between qualitative and...Ch. 1 - Explain the difference between a sample and a...Ch. 1 - Prob. 7CECh. 1 - For the following situations, would you collect...Ch. 1 - Exits along Interstate highways were formerly...
Ch. 1 - A poll solicits a large number of college...Ch. 1 - Barnes & Noble recently began selling an...Ch. 1 - Using the concepts of sample and population,...Ch. 1 - Place these variables in the following...Ch. 1 - AVX Home Entertainment, Inc., recently began a...Ch. 1 - The Wall Street Journal’s website, www.wsj.com,...Ch. 1 - The following chart depicts the average amounts...Ch. 1 - The following chart depicts the earnings in...Ch. 1 - Refer to the Real Estate data, which report...Ch. 1 - Refer to the Baseball 2012 data, which report...Ch. 1 - Refer to the Buena School District bus data, which...
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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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