EBK STATISTICAL TECHNIQUES IN BUSINESS
17th Edition
ISBN: 9781259924163
Author: Lind
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 13, Problem 4SR
To determine
Test whether the
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2. Which of the following statements are (not) true?
lim sup{An U Bn}
818
lim sup{A, B}
818
lim inf{An U Bn}
818
818
lim inf{A, B}
An
An A, Bn-
A, BnB
→B
=
=
=
lim sup A, U lim sup Bn;
818
818
lim sup A, lim sup Bn;
818
81U
lim inf A, U lim inf Bn;
818
818
lim inf A, lim inf Bn;
n→X
818
An U BRAUB
as no;
An OBRANB as n→∞.
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).
Chapter 13 Solutions
EBK STATISTICAL TECHNIQUES IN BUSINESS
Ch. 13 - Prob. 1SRCh. 13 - Prob. 1ECh. 13 - Prob. 2ECh. 13 - Bi-lo Appliance Super-Store has outlets in several...Ch. 13 - Prob. 4ECh. 13 - Prob. 5ECh. 13 - The owner of Maumee Ford-Volvo wants to study the...Ch. 13 - Prob. 2SRCh. 13 - Prob. 7ECh. 13 - Prob. 8E
Ch. 13 - Prob. 9ECh. 13 - Prob. 10ECh. 13 - Prob. 11ECh. 13 - Prob. 12ECh. 13 - Prob. 3SRCh. 13 - Prob. 13ECh. 13 - Prob. 14ECh. 13 - Prob. 15ECh. 13 - Prob. 16ECh. 13 - Prob. 17ECh. 13 - Prob. 18ECh. 13 - Prob. 19ECh. 13 - Prob. 20ECh. 13 - Prob. 4SRCh. 13 - Prob. 21ECh. 13 - Prob. 22ECh. 13 - Prob. 23ECh. 13 - Prob. 24ECh. 13 - Prob. 5SRCh. 13 - Prob. 25ECh. 13 - Prob. 26ECh. 13 - Prob. 27ECh. 13 - Prob. 28ECh. 13 - Prob. 29ECh. 13 - Prob. 30ECh. 13 - Prob. 6SRCh. 13 - Prob. 31ECh. 13 - Prob. 32ECh. 13 - Prob. 33ECh. 13 - Refer to Exercise 16. a. Determine the .95...Ch. 13 - Prob. 35ECh. 13 - Prob. 36ECh. 13 - A regional commuter airline selected a random...Ch. 13 - Prob. 38CECh. 13 - Prob. 39CECh. 13 - Prob. 40CECh. 13 - Prob. 41CECh. 13 - Prob. 42CECh. 13 - Prob. 43CECh. 13 - Prob. 44CECh. 13 - The manufacturer of Cardio Glide exercise...Ch. 13 - Prob. 46CECh. 13 - Prob. 47CECh. 13 - Prob. 48CECh. 13 - Prob. 49CECh. 13 - Mr. William Profit is studying companies going...Ch. 13 - Prob. 51CECh. 13 - Prob. 52CECh. 13 - Prob. 53CECh. 13 - Prob. 54CECh. 13 - A regression analysis relating the current market...Ch. 13 - Prob. 56CECh. 13 - Prob. 57CECh. 13 - A consumer buying cooperative tested the effective...Ch. 13 - Prob. 59CECh. 13 - Prob. 60CECh. 13 - TravelAir.com samples domestic airline flights to...Ch. 13 - The North Valley Real Estate data reports...Ch. 13 - Prob. 64DA
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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 aarrow_forwardExercise 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_forward
- 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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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