Statistics: The Art and Science of Learning from Data (4th Edition)
4th Edition
ISBN: 9780321997838
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Chapter 1, Problem 36CP
True or false? In a particular study, you could use
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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 1 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 1.1 - Aspirin and heart attacks The Harvard Medical...Ch. 1.1 - Poverty and race The Current Population Survey...Ch. 1.1 - GSS and heaven Go to the General Social Survey...Ch. 1.1 - GSS and heaven and hell Refer to the previous...Ch. 1.1 - GSS for subject you pick At the GSS website, click...Ch. 1.2 - Description and inference a. Distinguish between...Ch. 1.2 - Censorship The General Social Survey in 2012 asked...Ch. 1.2 - Concerned about global warming? The Institute for...Ch. 1.2 - Graduate school information Suppose a liberal arts...Ch. 1.2 - Prob. 10PB
Ch. 1.2 - Prob. 11PBCh. 1.2 - At what age did women marry? A historian wants to...Ch. 1.2 - Prob. 13PBCh. 1.2 - National service Consider the population of all...Ch. 1.2 - Samples vary less with more data Well see that the...Ch. 1.2 - Comparing polls The following table shows the...Ch. 1.2 - Prob. 18PBCh. 1.2 - Smoking cessation A study published in 2010 in The...Ch. 1.3 - Prob. 20PBCh. 1.3 - Shopping sales data file Construct a data file...Ch. 1.3 - Sample with caution Individuals with children who...Ch. 1.3 - Prob. 23PBCh. 1.3 - Use a data file with software You may need to...Ch. 1.3 - Prob. 25PBCh. 1.3 - Ebola outbreaks Ebola virus disease outbreaks have...Ch. 1 - UW Student survey In a University of Wisconsin...Ch. 1 - Euthanasia The General Social Survey asked, in...Ch. 1 - Prob. 30CPCh. 1 - Breaking down Brown versus Whitman Example 2 of...Ch. 1 - Online learning Your university is interested in...Ch. 1 - Prob. 33CPCh. 1 - Prob. 34CPCh. 1 - Prob. 35CPCh. 1 - True or false? In a particular study, you could...Ch. 1 - Prob. 39CPCh. 1 - Prob. 40CP
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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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