Essentials of Statistics (5th Edition)
5th Edition
ISBN: 9780321924599
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 1, Problem 1TP
Simple Random Sample In this project, we will use technology and randomness to identify a simple random sample. Let’s assume that we want to conduct a survey of people randomly selected from a population. Instead of using a very large population, we will refer to Data Set 12 in Appendix B for the list of 38 names of the presidents of the United States. (That list does not include presidents who took office as the result of a resignation or assassination.) We will use a process that results in a simple random sample of five of those names. The basic idea is to consider the list of 38 names to be numbered from 1 through 38. We will use technology to randomly generate five numbers between 1 and 38. and then we will identify the five names corresponding to those five random numbers.
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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 1 Solutions
Essentials of Statistics (5th Edition)
Ch. 1.2 - Statistical Significance versus Practical...Ch. 1.2 - Source of Data In conducting a statistical study,...Ch. 1.2 - Voluntary Response Sample What is a voluntary...Ch. 1.2 - Correlation and Causation What is meant by the...Ch. 1.2 - Consider the Source. In Exercises 5-8, determine...Ch. 1.2 - Consider the Source. In Exercises 5-8, determine...Ch. 1.2 - Consider the Source. In Exercises 5-8, determine...Ch. 1.2 - Consider the Source. In Exercises 5-8, determine...Ch. 1.2 - Sampling Method. In Exercises 9-12, determine...Ch. 1.2 - Sampling Method. In Exercises 9-12, determine...
Ch. 1.2 - Sampling Method. In Exercises 9-12, determine...Ch. 1.2 - Sampling Method. In Exercises 9-12, determine...Ch. 1.2 - Statistical Significance and Practical...Ch. 1.2 - Statistical Significance and Practical...Ch. 1.2 - Statistical Significance and Practical...Ch. 1.2 - Statistical Significance and Practical...Ch. 1.2 - In Exercises 17-20, refer to the data in the table...Ch. 1.2 - In Exercises 17-20, refer to the data in the table...Ch. 1.2 - Prob. 19BSCCh. 1.2 - Conclusion If we use the listed pulse rates with...Ch. 1.2 - In Exercises 21-24, refer to the data in the table...Ch. 1.2 - Prob. 22BSCCh. 1.2 - Prob. 23BSCCh. 1.2 - In Exercises 21-24, refer to the data in the table...Ch. 1.2 - Prob. 25BSCCh. 1.2 - Whats Wrong? In Exercises 25-28, identify what is...Ch. 1.2 - Whats Wrong? In Exercises 25-28, identify what is...Ch. 1.2 - Prob. 28BSCCh. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Prob. 32BSCCh. 1.2 - Percentages in Advertising An ad for Big Skinny...Ch. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Percentages in Advertising A New York Times...Ch. 1.2 - ATV Accidents The Associated Press provided an...Ch. 1.2 - Falsifying Data A researcher at the...Ch. 1.2 - Whats Wrong with This Picture? The Newport...Ch. 1.3 - Parameter and Statistic What is a parameter, and...Ch. 1.3 - Prob. 2BSCCh. 1.3 - Discrete/Continuous Data Which of the following...Ch. 1.3 - Identifying the Population In a Gallup poll of...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - Prob. 17BSCCh. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - Prob. 19BSCCh. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - Prob. 23BSCCh. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 29-32, identify the level of...Ch. 1.3 - In Exercises 29-32, identify the level of...Ch. 1.3 - In Exercises 29-32, identify the level of...Ch. 1.3 - In Exercises 29-32, identify the level of...Ch. 1.3 - Countable For each of the following, categorize...Ch. 1.3 - Scale for Rating Food A group of students develops...Ch. 1.3 - Interpreting Temperature Increase In the Born...Ch. 1.4 - Simple Random Sample At a national conference of...Ch. 1.4 - Observational Study and Experiment You want to...Ch. 1.4 - Simple Random Convenience Sample A student of the...Ch. 1.4 - Convenience Sample The author conducted a survey...Ch. 1.4 - In Exercises 5-8, determine whether the given...Ch. 1.4 - In Exercises 5-8, determine whether the given...Ch. 1.4 - In Exercises 5-8, determine whether the given...Ch. 1.4 - In Exercises 5-8, determine whether the given...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Prob. 23BSCCh. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Prob. 27BBCh. 1.4 - In Exercises 27-30, indicate whether the...Ch. 1.4 - In Exercises 27-30, indicate whether the...Ch. 1.4 - In Exercises 27-30, indicate whether the...Ch. 1.4 - In Exercises 31-34, identify which of these...Ch. 1.4 - In Exercises 31-34, identify which of these...Ch. 1.4 - Prob. 33BBCh. 1.4 - In Exercises 33-36, identify which of these...Ch. 1.4 - Blinding For the study described in Exercise 34,...Ch. 1.4 - Sample Design Literacy In Cardiovascular Effects...Ch. 1 - Chicago Bulls The numbers of the current players...Ch. 1 - Chicago Bulls Which of the following best...Ch. 1 - Earthquake Depths Data Set 16 includes depths (km)...Ch. 1 - Earthquake Depths Are the earthquake depths...Ch. 1 - Earthquake Depths Which of the following best...Ch. 1 - Earthquake Depths True or false: If you construct...Ch. 1 - Prob. 7CQQCh. 1 - Parameter and Statistic In a recent Gallup poll,...Ch. 1 - Observational Study or Experiment Are the data...Ch. 1 - 10. Statistical Significance and Practical...Ch. 1 - Walmart Stores Currently, there are 4227 Walmart...Ch. 1 - Whats Wrong? A survey sponsored by the American...Ch. 1 - Whats Wrong? A survey included 4230 responses from...Ch. 1 - Sampling Seventy-two percent of Americans squeeze...Ch. 1 - Percentages a. The labels on U-Turn protein energy...Ch. 1 - Why the Discrepancy? A Gallup poll was taken two...Ch. 1 - Statistical Significance and Practical...Ch. 1 - Marijuana Survey In a recent Pew poll of 1500...Ch. 1 - Marijuana Survey Identify the type of sampling...Ch. 1 - Marijuana Survey Exercise 8 referred to a Pew poll...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - Prob. 5CRECh. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - Simple Random Sample In this project, we will use...Ch. 1 - Critical Thinking The concept of six degrees of...Ch. 1 - Critical Thinking The concept of six degrees of...
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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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