EBK STATISTICAL TECHNIQUES IN BUSINESS
17th Edition
ISBN: 9781259924163
Author: Lind
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 11, Problem 43CE
To determine
Check whether there is a difference in the
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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 11 Solutions
EBK STATISTICAL TECHNIQUES IN BUSINESS
Ch. 11 - Tom Sevits is the owner of the Appliance Patch....Ch. 11 - Prob. 1ECh. 11 - Prob. 2ECh. 11 - Prob. 3ECh. 11 - As part of a study of corporate employees, the...Ch. 11 - Prob. 5ECh. 11 - Mary Jo Fitzpatrick is the vice president for...Ch. 11 - Prob. 2SRCh. 11 - Prob. 7ECh. 11 - For Exercises 7 and 8: (a) state the decision...
Ch. 11 - Prob. 9ECh. 11 - A recent study compared the time spent together by...Ch. 11 - Ms. Lisa Monnin is the budget director for Nexus...Ch. 11 - The Tampa Bay (Florida) Area Chamber of Commerce...Ch. 11 - It is often useful for companies to know who their...Ch. 11 - For exercises 13 and 14, assume the sample...Ch. 11 - Prob. 14ECh. 11 - Prob. 15ECh. 11 - Suppose you are an expert on the fashion industry...Ch. 11 - Prob. 4SRCh. 11 - Prob. 17ECh. 11 - Prob. 18ECh. 11 - Prob. 19ECh. 11 - Prob. 20ECh. 11 - Prob. 21CECh. 11 - Prob. 22CECh. 11 - Fry Brothers Heating and Air Conditioning Inc....Ch. 11 - A coffee manufacturer is interested in whether the...Ch. 11 - Prob. 25CECh. 11 - A computer manufacturer offers technical support...Ch. 11 - Prob. 27CECh. 11 - Prob. 28CECh. 11 - Prob. 29CECh. 11 - Prob. 30CECh. 11 - Prob. 31CECh. 11 - Prob. 32CECh. 11 - Prob. 33CECh. 11 - Prob. 34CECh. 11 - Prob. 35CECh. 11 - Prob. 36CECh. 11 - Prob. 37CECh. 11 - Prob. 38CECh. 11 - Prob. 39CECh. 11 - Prob. 40CECh. 11 - An investigation of the effectiveness of an...Ch. 11 - Prob. 42CECh. 11 - Prob. 43CECh. 11 - Prob. 44CECh. 11 - Prob. 45CECh. 11 - Prob. 46CECh. 11 - Prob. 47DACh. 11 - Prob. 49DA
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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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