EBK STATISTICAL TECHNIQUES IN BUSINESS
17th Edition
ISBN: 9781259924163
Author: Lind
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 8, Problem 18E
a.
To determine
Find the standard error of the
b.
To determine
Find the likelihood the sample mean is greater than 320 minutes.
c.
To determine
Find the likelihood the sample mean is between 320 and 350 minutes.
d.
To determine
Find the likelihood the sample mean is greater than 350 minutes.
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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 8 Solutions
EBK STATISTICAL TECHNIQUES IN BUSINESS
Ch. 8 - Prob. 1SRCh. 8 - Prob. 2SRCh. 8 - The following is a list of 24 Marcos Pizza stores...Ch. 8 - The following is a list of 29 hospitals in the...Ch. 8 - Listed below are the 35 members of the Metro...Ch. 8 - Listed next are the 27 Nationwide Insurance agents...Ch. 8 - The years of service of the five executives...Ch. 8 - Prob. 5ECh. 8 - Prob. 6ECh. 8 - Prob. 7E
Ch. 8 - Prob. 8ECh. 8 - Prob. 9ECh. 8 - There are five sales associates at Mid-Motors...Ch. 8 - Prob. 4SRCh. 8 - Prob. 11ECh. 8 - Prob. 12ECh. 8 - Prob. 5SRCh. 8 - Prob. 15ECh. 8 - Prob. 16ECh. 8 - Prob. 17ECh. 8 - Prob. 18ECh. 8 - Prob. 19CECh. 8 - The Medical Assurance Company is investigating the...Ch. 8 - Prob. 21CECh. 8 - Prob. 22CECh. 8 - Prob. 23CECh. 8 - Prob. 24CECh. 8 - Prob. 25CECh. 8 - As a part of their customer-service program,...Ch. 8 - Prob. 27CECh. 8 - Prob. 28CECh. 8 - Prob. 29CECh. 8 - The Appliance Center has six sales representatives...Ch. 8 - Prob. 31CECh. 8 - Prob. 32CECh. 8 - Prob. 33CECh. 8 - Prob. 34CECh. 8 - Prob. 35CECh. 8 - A recent study by the Greater Los Angeles Taxi...Ch. 8 - Prob. 37CECh. 8 - Prob. 38CECh. 8 - Prob. 39CECh. 8 - Prob. 40CECh. 8 - Prob. 41CECh. 8 - Human Resource Consulting (HRC) surveyed a random...Ch. 8 - Over the past decade, the mean number of hacking...Ch. 8 - Prob. 44CECh. 8 - Prob. 45CECh. 8 - Prob. 46DACh. 8 - Prob. 47DACh. 8 - Prob. 48DA
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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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