Intro Stats
4th Edition
ISBN: 9780321826275
Author: Richard D. De Veaux
Publisher: PEARSON
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Chapter 20, Problem 48E
Carbs Recently, the Gallup Poll asked 1005 U.S. adults if they actively try to avoid carbohydrates in their diet. That number increased to 27% from 20% in a similar 2002 poll. Is this a statistically significant increase? Explain.
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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 20 Solutions
Intro Stats
Ch. 20.3 - A public broadcasting station plans to launch a...Ch. 20.3 - Prob. 2JCCh. 20.4 - Prob. 3JCCh. 20.4 - Prob. 4JCCh. 20.5 - Prob. 5JCCh. 20.5 - Prob. 6JCCh. 20.5 - Prob. 7JCCh. 20.5 - Prob. 8JCCh. 20.6 - Prob. 9JCCh. 20.6 - Recall the experiment comparing patients 4 weeks...
Ch. 20.6 - Prob. 11JCCh. 20 - Canada Suppose an advocacy organization surveys...Ch. 20 - Non-profits Do people who work for non-profit...Ch. 20 - Prob. 3ECh. 20 - Prob. 4ECh. 20 - Canada, deux The information in Exercise 1 was...Ch. 20 - Prob. 6ECh. 20 - Prob. 7ECh. 20 - Prob. 8ECh. 20 - Prob. 9ECh. 20 - Prob. 10ECh. 20 - Prob. 11ECh. 20 - Prob. 12ECh. 20 - Prob. 13ECh. 20 - Athlete ages, again Using the summary statistics...Ch. 20 - Prob. 15ECh. 20 - Athlete ages, ninth inning The researchers in...Ch. 20 - Prob. 17ECh. 20 - Athlete ages, overtime Repeat the test you did in...Ch. 20 - Prob. 19ECh. 20 - Prob. 20ECh. 20 - Prob. 21ECh. 20 - Prob. 22ECh. 20 - Prob. 23ECh. 20 - Prob. 24ECh. 20 - Prob. 25ECh. 20 - Prob. 26ECh. 20 - Prob. 27ECh. 20 - Graduation The U.S. Department of Commerce...Ch. 20 - Prob. 29ECh. 20 - Carpal tunnel The painful wrist condition called...Ch. 20 - Prob. 31ECh. 20 - Prob. 32ECh. 20 - Ear infections A new vaccine was recently tested...Ch. 20 - Anorexia The Journal of the American Medical...Ch. 20 - Prob. 35ECh. 20 - Prob. 36ECh. 20 - Teen smoking A Vermont study published by the...Ch. 20 - Depression A study published in the Archives of...Ch. 20 - Birthweight The Journal of the American Medical...Ch. 20 - Politics and sex One month before the election, a...Ch. 20 - Prob. 41ECh. 20 - Prob. 42ECh. 20 - Pain Researchers comparing the effectiveness of...Ch. 20 - Gender gap Candidates for political office realize...Ch. 20 - Prob. 45ECh. 20 - Prob. 46ECh. 20 - Sensitive men In the same article from Exercise...Ch. 20 - Carbs Recently, the Gallup Poll asked 1005 U.S....Ch. 20 - Food preference GfK Roper Consulting gathers...Ch. 20 - Prob. 50ECh. 20 - Hot dogs In the July 2007 issue, Consumer Reports...Ch. 20 - Prob. 52ECh. 20 - Prob. 53ECh. 20 - Prob. 54ECh. 20 - Hot dogs, last one In Exercise 53, we saw a 90%...Ch. 20 - Third load of wash In Exercise 54, we saw a 98%...Ch. 20 - Prob. 57ECh. 20 - Prob. 58ECh. 20 - Prob. 59ECh. 20 - Prob. 60ECh. 20 - Commuting A man who moves to a new city sees that...Ch. 20 - Pulse rates A researcher wanted to see whether...Ch. 20 - 63. View of the water How much extra is having a...Ch. 20 - New construction The house sales we looked at in...Ch. 20 - Cereal sugar The data below show the sugar content...Ch. 20 - Prob. 66ECh. 20 - Prob. 67ECh. 20 - Prob. 68ECh. 20 - Prob. 69ECh. 20 - Prob. 70ECh. 20 - Prob. 71ECh. 20 - Prob. 72ECh. 20 - Prob. 73ECh. 20 - Prob. 74ECh. 20 - Prob. 75ECh. 20 - Ad campaign You are a consultant to the marketing...Ch. 20 - Prob. 77ECh. 20 - Thirsty? Researchers randomly assigned...Ch. 20 - Prob. 79ECh. 20 - Prob. 80ECh. 20 - 81. Running heats In Olympic running events,...Ch. 20 - Prob. 82ECh. 20 - Tees Does it matter what kind of tee a golfer...Ch. 20 - Golf again Given the test results on golf tees...Ch. 20 - Music and memory Is it a good idea to listen to...Ch. 20 - Rap Using the results of the experiment described...
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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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