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 30CP
To determine
Explain how the given margin of error provides an
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(b) Define a simple random variable. Provide an example.
17. (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.
16. (a) Show that IA(w) is a random variable if and only if A E F
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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- 15. 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_forward
- 7. (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_forward18. Define a bivariate random variable. Provide an example.arrow_forward
- 6. (a) Let (, F, P) be a probability space. Explain when a subset of ?? is measurable and why. (b) Define a probability measure. (c) Using the probability axioms, show that if AC B, then P(A) < P(B). (d) Show that P(AUB) + P(A) + P(B) in general. Write down and prove the formula for the probability of the union of two sets.arrow_forward21. Prove that: {(a, b), - sa≤barrow_forward10. (a) Define the independence of sets A, B, C. (b) Provide an example where A, B, C are pairwise independent but not mutually independent. (c) Give an example where P(AnBnC) = P(A)P(B)P(C), but the sets are not pairwise independent.arrow_forward23. State Bayes' formula. Jaching R. Machine.arrow_forward(d) Show that A, and A' are tail events.arrow_forward11. (a) Define the (mathematical and conceptual) definition of conditional probability P(A|B). (b) Explain the product law in conditional probability. (c) Explain the relation between independence and the conditional probability of two sets.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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