Introductory Statistics
3rd Edition
ISBN: 9780135188927
Author: Gould, Robert, Ryan, Colleen N. (colleen Nooter)
Publisher: Pearson,
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Chapter 13, Problem 7SE
a.
To determine
Find the log (base 10) of the numbers
b.
To determine
Find the antilog (base 10) of the numbers
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17. Suppose that X1, X2,..., Xn are random variables, such that E|xk| < ∞ for
all k, and set Yn = max1
6. Show that, for any random variable, X, and a > 0,
L
P(x < X ≤ x+a) dx = a.
2015
15. This problem extends Problem 20.6. Let X, Y be random variables with finite
mean. Show that
(P(X ≤ x ≤ Y) - P(Y < x ≤ X))dx = E Y — E X.
Chapter 13 Solutions
Introductory Statistics
Ch. 13 - What is the fundamental condition required for...Ch. 13 - In what situations are nonparametric statistics...Ch. 13 - In addition to random samples, what other...Ch. 13 - What summary statistics are best used to report...Ch. 13 - Prob. 5SECh. 13 - Prob. 6SECh. 13 - Prob. 7SECh. 13 - Log Transforms a. Find the log (base 10) of each...Ch. 13 - Prob. 9SECh. 13 - Prob. 10SE
Ch. 13 - Prob. 11SECh. 13 - Morning Routine A statistics student conducted a...Ch. 13 - Exercise Hours A statistics student was interested...Ch. 13 - Television Viewing A Nielsen poll asked people the...Ch. 13 - Lead Exposure (Example 3) Excessive lead levels...Ch. 13 - Juvenile Delinquents Dr. Kirkland R. Gable (in...Ch. 13 - The Stroop Effect Suppose you had to identify the...Ch. 13 - Reading Material on Colored Paper In the past,...Ch. 13 - Males’ Pulse Rates Students in a statistics class...Ch. 13 - Females’ Pulse Rates Refer to exercise 13.19. This...Ch. 13 - Ages of Brides and Grooms A random sample of the...Ch. 13 - Textbook Prices A student was interested in...Ch. 13 - Meat-Eating Behavior (Example 4) A researcher was...Ch. 13 - Credit Card Debt A statistics student who was...Ch. 13 - Prob. 25SECh. 13 - Sleep Typically, do men and women sleep different...Ch. 13 - Cell Phone Bills Cell phone bills (rounded to the...Ch. 13 - Weights of Athletes Data were collected on the...Ch. 13 - Happiness A StatCrunch survey of happiness...Ch. 13 - Soda A StatCrunch survey was done asking what...Ch. 13 - Sports and Extraversion (Example 5) Are students...Ch. 13 - Happiness Are women happier than men? A StatCrunch...Ch. 13 - College Students and Credit Card Debt In exercise...Ch. 13 - Soda Does soda constitute a larger part of the...Ch. 13 - Rainfall In a well-known study on the effects of...Ch. 13 - Rainfall Refer to exercise 13.35, which discussed...Ch. 13 - Randomization Exercise 13.35 describes a...Ch. 13 - Randomization Exercise 13.35 describes a...Ch. 13 - Prob. 39CRECh. 13 - For exercises 13.39 through 13.46, choose from the...Ch. 13 - Prob. 41CRECh. 13 - For exercises 13.39 through 13.46, choose from the...Ch. 13 - Prob. 43CRECh. 13 - Prob. 44CRECh. 13 - For exercises 13.39 through 13.46, choose from the...Ch. 13 - For exercises 13.39 through 13.46, choose from the...Ch. 13 - Ice Cream Cones McDonald’s claims that its ice...Ch. 13 - Average Body Temperatures Many people believe that...Ch. 13 - Contacting Mom Random samples of 30 professors of...Ch. 13 - 13.50 through 13.54 Texts Sent and Received...Ch. 13 - 13.50 through 13.54 Texts Sent and Received...Ch. 13 - 13.50 through 13.54 Texts Sent and Received...Ch. 13 - 13.50 through 13.54 Texts Sent and Received...Ch. 13 - 13.50 through 13.54 Texts Sent and Received...Ch. 13 - Geometric Mean The dotplot shows the number of...Ch. 13 - Looking at the data about contacting mom (exercise...Ch. 13 - Resampling Moms We performed a randomization test...Ch. 13 - Prob. 58CRECh. 13 - Prob. 59CRECh. 13 - Prob. 60CRE
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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→∞.arrow_forwardThroughout, 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).arrow_forward16. 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).arrow_forward
- 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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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