Pearson eText Introductory Statistics: Exploring the World Through Data -- Instant Access (Pearson+)
3rd Edition
ISBN: 9780136880882
Author: Robert Gould, Rebecca Wong
Publisher: PEARSON+
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Chapter 12, Problem 9SE
a.
To determine
Determine the treatment and response variables in the given study.
b.
To determine
Give the conclusion of the study in terms of cause and effect relation and explain the reason for concluding the cause and effect relationship from the study.
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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 12 Solutions
Pearson eText Introductory Statistics: Exploring the World Through Data -- Instant Access (Pearson+)
Ch. 12 - Dairy Products and Muscle The following two...Ch. 12 - Coffee and Depression The following two headlines...Ch. 12 - Marijuana Use and Bone Density In a 2017 study...Ch. 12 - Prob. 4SECh. 12 - Prob. 5SECh. 12 - Prob. 6SECh. 12 - Prob. 7SECh. 12 - Smoking Cessation In a 2018 study reported in The...Ch. 12 - Prob. 9SECh. 12 - Prob. 10SE
Ch. 12 - Prob. 11SECh. 12 - Sugary Drinks and Brain Health An April 2017...Ch. 12 - Expression of Feelings A 2017 Pew poll asked a...Ch. 12 - Prob. 14SECh. 12 - Prob. 15SECh. 12 - SAT Prep and Power Suppose an SAT tutoring company...Ch. 12 - Brain Games (Example 2) Researchers are interested...Ch. 12 - A Smile a Day Smiling is a sign of a good mood,...Ch. 12 - Speed Skating Suits (Example 3) Speed skating is a...Ch. 12 - Flu Vaccines and Age Suppose you want to compare...Ch. 12 - Preventing Heart Attacks with Aspirin Suppose that...Ch. 12 - Prob. 22SECh. 12 - Dietary Improvement and Depression In a 2017...Ch. 12 - Prob. 24SECh. 12 - Reading Colored Paper (Example 4) Some people...Ch. 12 - Prob. 26SECh. 12 - Prob. 27SECh. 12 - Prob. 28SECh. 12 - Prob. 29SECh. 12 - Library Audio Books Suppose a college is deciding...Ch. 12 - Prob. 31SECh. 12 - Prob. 32SECh. 12 - Prob. 33SECh. 12 - Prob. 34SECh. 12 - Prob. 35SECh. 12 - Prob. 36SECh. 12 - Prob. 37SECh. 12 - Prob. 38SECh. 12 - Prob. 39SECh. 12 - Prob. 40SECh. 12 - Prob. 41SECh. 12 - Prob. 42SECh. 12 - Prob. 43SECh. 12 - Prob. 44SECh. 12 - Yoga Study Design Refer to exercise 12.43. How...Ch. 12 - Fish Consumption Study Design Refer to exercise...Ch. 12 - Prob. 47SECh. 12 - Prob. 48SECh. 12 - Alumni Donations The alumni office wishes to...Ch. 12 - Prob. 50SECh. 12 - Prob. 51SECh. 12 - Prob. 52SECh. 12 - For exercises 12.51-12.53, evaluate the study...Ch. 12 - Prob. 54SECh. 12 - Anesthesia Care and Adverse Postoperative Outcomes...Ch. 12 - Prob. 56SECh. 12 - Prob. 57SECh. 12 - Prob. 58SE
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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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