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 19.2, Problem 6E
A quality control process monitors the weight per carton of laundry detergent. Control limits are set at UCL = 20.12 ounces and LCL = 19.90 ounces.
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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 19 Solutions
Statistics for Business & Economics, Revised (MindTap Course List)
Ch. 19.2 - A process that is in control has a mean of = 12.5...Ch. 19.2 - Twenty-five samples, each of size 5, were selected...Ch. 19.2 - Twenty-five samples of 100 items each were...Ch. 19.2 - A process sampled 20 times with a sample of size 8...Ch. 19.2 - Temperature is used to measure the output of a...Ch. 19.2 - A quality control process monitors the weight per...Ch. 19.2 - The Goodman Tire and Rubber Company periodically...Ch. 19.2 - Over several weeks of normal, or in-control,...Ch. 19.2 - An airline operates a call center to handle...Ch. 19.3 - For an acceptance sampling plan with n = 25 and c...
Ch. 19.3 - Consider an acceptance sampling plan with n = 20...Ch. 19.3 - Repeat exercise 11 for the acceptance sampling...Ch. 19.3 - Refer to the KALI problem presented in this...Ch. 19.3 - To inspect incoming shipments of raw materials, a...Ch. 19.3 - A domestic manufacturer of watches purchases...Ch. 19 - Samples of size 5 provided the following 20 sample...Ch. 19 - Product filling weights are normally distributed...Ch. 19 - Twenty-five samples of size 5 resulted in x = 5.42...Ch. 19 - The following are quality control data for a...Ch. 19 - The following were collected for the Master Blend...Ch. 19 - An insurance company samples claim forms for...Ch. 19 - Managers of 1200 different retail outlets make...Ch. 19 - An n = 10, c = 2 acceptance sampling plan is being...Ch. 19 - Prob. 24SECh. 19 - A manufacturer produces lots of a canned food...
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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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