Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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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 2 Solutions
Introductory Statistics (10th Edition)
Ch. 2.1 - Give an example, other than those presented in...Ch. 2.1 - Explain the meaning of a. qualitative variable. b....Ch. 2.1 - Explain the meaning of a. qualitative data. b....Ch. 2.1 - Provide a reason why the classification of data is...Ch. 2.1 - Of the variables you have studied so far, which...Ch. 2.1 - For each part of Exercises 2.62.11, classify the...Ch. 2.1 - Earthquakes. The U.S. Geological Survey monitors...Ch. 2.1 - Top 10 IPOs. An online article from the Washington...Ch. 2.1 - Earnings from the Crypt. On the Celebrity NetWorth...Ch. 2.1 - World University Rankings. The Times Higher...
Ch. 2.1 - Recording Industry Statistics. The Recording...Ch. 2.1 - RBI Kings. As reported on MLB.com, the five...Ch. 2.1 - Top Broadcast Shows. As reported in Primetime...Ch. 2.1 - The Fulbright Program. The U.S. governments...Ch. 2.1 - Top 10 Green Cars. The following table presents...Ch. 2.1 - Ordinal Data. Another important type of data is...Ch. 2.2 - What is a frequency distribution of qualitative...Ch. 2.2 - Explain the difference between a. frequency and...Ch. 2.2 - Answer true or false to each of the statements in...Ch. 2.2 - In Exercises 2.202.25, we have presented some...Ch. 2.2 - Prob. 21ECh. 2.2 - In Exercises 2.202.25, we have presented some...Ch. 2.2 - Prob. 23ECh. 2.2 - In Exercises 2.202.25, we have presented some...Ch. 2.2 - In Exercises 2.202.25, we have presented some...Ch. 2.2 - For each data set in Exercises 2.262.31, a....Ch. 2.2 - For each data set in Exercises 2.262.31, a....Ch. 2.2 - For each data set in Exercises 2.262.31, a....Ch. 2.2 - For each data set in Exercises 2.262.31, a....Ch. 2.2 - For each data set in Exercises 2.262.31, a....Ch. 2.2 - For each data set in Exercises 2.262.31, a....Ch. 2.2 - In each of Exercises 2.322.37, we have presented a...Ch. 2.2 - In each of Exercises 2.322.37, we have presented a...Ch. 2.2 - In each of Exercises 2.322.37, we have presented a...Ch. 2.2 - In each of Exercises 2.322.37, we have presented a...Ch. 2.2 - In each of Exercises 2.322.37, we have presented a...Ch. 2.2 - Prob. 37ECh. 2.2 - Health Status. The National Center for Health...Ch. 2.2 - In Exercises 2.392.41, use the technology of your...Ch. 2.2 - Prob. 40ECh. 2.2 - In Exercises 2.392.41, use the technology of your...Ch. 2.3 - Identify an important reason for grouping data.Ch. 2.3 - Do the concepts of class limits, marks, cutpoints,...Ch. 2.3 - State three of the most important guidelines in...Ch. 2.3 - With regard to grouping quantitative data into...Ch. 2.3 - For quantitative data, we examined three types of...Ch. 2.3 - We used slightly different methods for determining...Ch. 2.3 - Explain the difference between a frequency...Ch. 2.3 - Explain the advantages and disadvantages of...Ch. 2.3 - For data that are grouped in classes based on more...Ch. 2.3 - Discuss the relative advantages and disadvantages...Ch. 2.3 - Suppose that you have a data set that contains a...Ch. 2.3 - Suppose that you have constructed a stem-and-leaf...Ch. 2.3 - In each of Exercises 2.542.59, we have presented a...Ch. 2.3 - In each of Exercises 2.542.59, we have presented a...Ch. 2.3 - In each of Exercises 2.542.59, we have presented a...Ch. 2.3 - In each of Exercises 2.542.59, we have presented a...Ch. 2.3 - Prob. 58ECh. 2.3 - In each of Exercises 2.542.59, we have presented a...Ch. 2.3 - Prob. 60ECh. 2.3 - Prob. 61ECh. 2.3 - In Exercises 2.602.71, we have presented some...Ch. 2.3 - In Exercises 2.602.71, we have presented some...Ch. 2.3 - In Exercises 2.602.71, we have presented some...Ch. 2.3 - In Exercises 2.602.71, we have presented some...Ch. 2.3 - Prob. 66ECh. 2.3 - In Exercises 2.602.71, we have presented some...Ch. 2.3 - In Exercises 2.602.71, we have presented some...Ch. 2.3 - Prob. 69ECh. 2.3 - In Exercises 2.602.71, we have presented some...Ch. 2.3 - In Exercises 2.602.71, we have presented some...Ch. 2.3 - Prob. 72ECh. 2.3 - In each of Exercises 2.722.75, construct a dotplot...Ch. 2.3 - Prob. 74ECh. 2.3 - In each of Exercises 2.722.75, construct a dotplot...Ch. 2.3 - In each of Exercises 2.762.79, construct a...Ch. 2.3 - Prob. 77ECh. 2.3 - In each of Exercises 2.762.79, construct a...Ch. 2.3 - Prob. 79ECh. 2.3 - Prob. 80ECh. 2.3 - For each data set in Exercises 2.802.91, use the...Ch. 2.3 - For each data set in Exercises 2.802.91, use the...Ch. 2.3 - For each data set in Exercises 2.802.91, use the...Ch. 2.3 - For each data set in Exercises 2.802.91, use the...Ch. 2.3 - For each data set in Exercises 2.802.91, use the...Ch. 2.3 - For each data set in Exercises 2.802.91, use the...Ch. 2.3 - Prob. 87ECh. 2.3 - Prob. 88ECh. 2.3 - Prob. 89ECh. 2.3 - Prob. 90ECh. 2.3 - Prob. 91ECh. 2.3 - Prob. 92ECh. 2.3 - Age of Passenger Cars. According to R. L. Polk ...Ch. 2.3 - Stressed-Out Bus Drivers. Frustrated passengers,...Ch. 2.3 - Acute Postoperative Days. Several neurosurgeons...Ch. 2.3 - MMs. In the article Sweetening StatisticsWhat MMs...Ch. 2.3 - Women in the Workforce. In an issue of Science...Ch. 2.3 - Process Capability. R. Morris and E. Watson...Ch. 2.3 - University Patents. The number of patents a...Ch. 2.3 - Prob. 100ECh. 2.3 - Prob. 101ECh. 2.3 - Adjusted Gross Incomes. The Internal Revenue...Ch. 2.3 - Cholesterol Levels. According to the National...Ch. 2.3 - Hospital Beds. The number of hospital beds...Ch. 2.3 - Parkinsons Disease. Parkinsons disease affects...Ch. 2.3 - The Great White Shark. In an article titled Great...Ch. 2.3 - The Beatles. In the article, Length of The Beatles...Ch. 2.3 - High School Completion. As reported by the U.S....Ch. 2.3 - Prob. 109ECh. 2.3 - Body Temperature. A study by researchers at the...Ch. 2.3 - Exam Scores. The exam scores for the students in...Ch. 2.3 - Prob. 112ECh. 2.3 - Prob. 113ECh. 2.3 - Age and Gender. The following bivariate data on...Ch. 2.3 - Prob. 115ECh. 2.3 - Clocking the Cheetah. Construct a...Ch. 2.3 - Prob. 117ECh. 2.3 - Residential Energy Consumption. Refer to the...Ch. 2.3 - Prob. 119ECh. 2.3 - Cardiovascular Hospitalizations. The Florida State...Ch. 2.3 - Prob. 121ECh. 2.4 - In each of Exercises 2.1222.127, explain the...Ch. 2.4 - In each of Exercises 2.1222.127, explain the...Ch. 2.4 - In each of Exercises 2.1222.127, explain the...Ch. 2.4 - Prob. 125ECh. 2.4 - Prob. 126ECh. 2.4 - Prob. 127ECh. 2.4 - Prob. 128ECh. 2.4 - Suppose that a variable of a population has a...Ch. 2.4 - Prob. 130ECh. 2.4 - Identify and sketch three distribution shapes that...Ch. 2.4 - Prob. 132ECh. 2.4 - In each of Exercises 2.1322.139, we have drawn a...Ch. 2.4 - In each of Exercises 2.1322.139, we have drawn a...Ch. 2.4 - In each of Exercises 2.1322.139, we have drawn a...Ch. 2.4 - In each of Exercises 2.1322.139, we have drawn a...Ch. 2.4 - In each of Exercises 2.1322.139, we have drawn a...Ch. 2.4 - In each of Exercises 2.1322.139, we have drawn a...Ch. 2.4 - Prob. 139ECh. 2.4 - In each of Exercises 2.1402.149, we have provided...Ch. 2.4 - In each of Exercises 2.1402.149, we have provided...Ch. 2.4 - Prob. 142ECh. 2.4 - In each of Exercises 2.1402.149, we have provided...Ch. 2.4 - In each of Exercises 2.1402.149, we have provided...Ch. 2.4 - In each of Exercises 2.1402.149, we have provided...Ch. 2.4 - In each of Exercises 2.1402.149, we have provided...Ch. 2.4 - Prob. 147ECh. 2.4 - Prob. 148ECh. 2.4 - Prob. 149ECh. 2.4 - Old Faithful. Old Faithful is a geyser in...Ch. 2.4 - SnowGoose Nests. In the article Trophic...Ch. 2.4 - Prob. 152ECh. 2.4 - In each of Exercises 2.1522.157, a. use the...Ch. 2.4 - In each of Exercises 2.1522.157, a. use the...Ch. 2.4 - Prob. 155ECh. 2.4 - In each of Exercises 2.1522.157, a. use the...Ch. 2.4 - In each of Exercises 2.1522.157, a. use the...Ch. 2.4 - Standard Normal Distribution. One of the most...Ch. 2.5 - Give one reason why constructing and reading...Ch. 2.5 - Prob. 163ECh. 2.5 - Reading Skills. Each year the director of the...Ch. 2.5 - Americas Melting Pot. The U.S. Census Bureau...Ch. 2.5 - Prob. 167ECh. 2.5 - Drunk-Driving Fatalities. Drunk-driving fatalities...Ch. 2.5 - Prob. 169ECh. 2.5 - Prob. 170ECh. 2.5 - Prob. 171ECh. 2 - This problem is about variables. a. What is a...Ch. 2 - This problem is about data. a. What are data? b....Ch. 2 - For a qualitative data set, what is a a. frequency...Ch. 2 - What is the relationship between a frequency or...Ch. 2 - Identify two main types of graphical displays that...Ch. 2 - In a bar chart, unlike in a histogram, the bars do...Ch. 2 - Some users of statistics prefer pie charts to bar...Ch. 2 - When is the use of single-value grouping...Ch. 2 - A quantitative data set has been grouped by using...Ch. 2 - A quantitative data set has been grouped by using...Ch. 2 - A quantitative data set has been grouped by using...Ch. 2 - A quantitative data set has been grouped by using...Ch. 2 - Explain the relative positioning of the bars in a...Ch. 2 - Sketch the curve corresponding to each of the...Ch. 2 - Draw a smooth curve that represents a symmetric...Ch. 2 - Prob. 16RPCh. 2 - Largest Hydroelectric Plants. According to...Ch. 2 - DVD Players. Refer to Example 2.16 on page 60. a....Ch. 2 - Inauguration Ages. From the Information Please...Ch. 2 - Inauguration Ages. Refer to Problem 19. Construct...Ch. 2 - Prob. 21RPCh. 2 - Prob. 22RPCh. 2 - Busy Bank Tellers. The Prescott National Bank has...Ch. 2 - On-Time Arrivals. The Air Travel Consumer Report...Ch. 2 - Old Ballplayers. From the ESPN Web site, we...Ch. 2 - Prob. 26RPCh. 2 - U.S. Divisions. The U.S. Census Bureau divides the...Ch. 2 - Prob. 28RPCh. 2 - Prob. 29RPCh. 2 - Hair and Eye Color. In the article Graphical...Ch. 2 - Prob. 31RPCh. 2 - In Problems 3133, a. identify the population and...Ch. 2 - In Problems 3133, a. identify the population and...Ch. 2 - UWEC UNDERGRADUATES Recall from Chapter 1 (see...Ch. 2 - Recall that, each year, Forbes magazine publishes...
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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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