Basic Business Statistics, Student Value Edition
14th Edition
ISBN: 9780134685113
Author: Mark L. Berenson, David M. Levine, David F. Stephan, Kathryn Szabat
Publisher: PEARSON
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Chapter 2, Problem 86PS
To determine
Write the difference between the drill down and slicer.
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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
Basic Business Statistics, Student Value Edition
Ch. 2 - A categorical variable has three categories, with...Ch. 2 - The following data represent the responses to two...Ch. 2 - The following table, stored in Smartphones Sales,...Ch. 2 - The Consumer Financial Protection Bureau reports...Ch. 2 - In addition to the impact of Big Data, what...Ch. 2 - This table represents the summer power-generating...Ch. 2 - Timetric’s 2016 survey of insurance...Ch. 2 - A survey of 1,520 Americans adults asked “Do you...Ch. 2 - A study of selected Kickstarter projects showed...Ch. 2 - Do special recommendations increase ad...
Ch. 2 - Construct an ordered array, given the following...Ch. 2 - Construct an ordered array, given the following...Ch. 2 - Planning and preparing for the unexpected,...Ch. 2 - Data was collected on salaries of compliance...Ch. 2 - The file NBACost contains the total cost ($ ) for...Ch. 2 - The file Utility contains the following data about...Ch. 2 - How much time do commuters living in or near...Ch. 2 - How do the average credit scores of people living...Ch. 2 - One operation of a mill is to cut pieces of steel...Ch. 2 - Call centers today play an important role in...Ch. 2 - The financial service call centre in problem 2.20...Ch. 2 - The file Bulbs contains the life (in hours) of a...Ch. 2 - The file Drink Contains the following data for the...Ch. 2 - A survey of online shoppers revealed that in 2015...Ch. 2 - How do college students spend their day? The 2016...Ch. 2 - The Energy Information Administration reported the...Ch. 2 - The Consumer Financial Protection Bureau reports...Ch. 2 - The following table indicates the percentage of...Ch. 2 - Timetric’s 2016 survey of insurance...Ch. 2 - A survey of 1,520 American adults asked “Do you...Ch. 2 - A study of selected Kickstarter projects showed...Ch. 2 - Do special recommendations increase ad...Ch. 2 - Construct a stern-and-leaf display, given the...Ch. 2 - Construct an ordered array, given the following...Ch. 2 - The following is a stern-and0-leaf display...Ch. 2 - The file NBACost contains the total cost in$ for...Ch. 2 - The file MobileSpeed contains the overall download...Ch. 2 - The file Utility contains the following data about...Ch. 2 - As player salaries have increases, the cost of...Ch. 2 - The following histogram and cumulative percentage...Ch. 2 - How much time do Americans living in cities spend...Ch. 2 - How do the average credit scores of people living...Ch. 2 - One operation of a mill is to cut pieces of steel...Ch. 2 - Call centers today play an important role in...Ch. 2 - The financial service call center in problem 2.44...Ch. 2 - The file Bulbs contains the life (in hours) of a...Ch. 2 - The data stored in Drink represents the amount of...Ch. 2 - The following is a set of data from a sample of...Ch. 2 - The following is a series of annual sales...Ch. 2 - Movie companies need to predict the gross receipts...Ch. 2 - Data were collected on the typical cost of dining...Ch. 2 - The file Mobile contains the overall download and...Ch. 2 - A Pew Research Center survey found a noticeable...Ch. 2 - How have stocks performed in the past? The...Ch. 2 - The file NewHomeSales contains the number of new...Ch. 2 - The file Movie Attendance 16 contains the yearly...Ch. 2 - The Super Bowl is a big viewing event watched by...Ch. 2 - Using the sample of retirement funds stored in...Ch. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 60PSCh. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 62PSCh. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 64PSCh. 2 - Using the sample of retirement funds stored in...Ch. 2 - Prob. 66PSCh. 2 - Prob. 67PSCh. 2 - Prob. 68PSCh. 2 - Prob. 71PSCh. 2 - Prob. 72PSCh. 2 - Examine the following visualization, adapted from...Ch. 2 - Prob. 75PSCh. 2 - Prob. 76PSCh. 2 - How do histograms and polygons differ in...Ch. 2 - Why would you construct a summary table?Ch. 2 - What are the advantages and disadvantage of using...Ch. 2 - Compare and contrast the bar chart for categorical...Ch. 2 - What is the difference between a time-series plot...Ch. 2 - Why is it said that the main feature of a Pareto...Ch. 2 - What are the three different ways to break down...Ch. 2 - How can a multidimensional table differ from a...Ch. 2 - What type of insights can you gain from a...Ch. 2 - Prob. 86PSCh. 2 - What is the difference between a time-series plot...Ch. 2 - The following table shown in the TextbookCosts...Ch. 2 - The following table represents the market share...Ch. 2 - B2B marketers in North America were surveyed about...Ch. 2 - The owner of a restaurant that services...Ch. 2 - Suppose that the owner of the restaurant in...Ch. 2 - The following data represents the pounds per...Ch. 2 - The Air Travel Consumer Report, a monthly product...Ch. 2 - One of the major measures of the quality of...Ch. 2 - The file DomesticBeer Contains the percentage...Ch. 2 - Prob. 97PSCh. 2 - The file CDRate contains the yields for one-year...Ch. 2 - The file CEO 2016 includes the total compensation...Ch. 2 - Prob. 100PSCh. 2 - What was the average price of a room at two-star,...Ch. 2 - The file Protein contains calorie and cholesterol...Ch. 2 - The file Natural Gas contains the U.S. monthly...Ch. 2 - The data stored in Drink represent the amount of...Ch. 2 - Prob. 105PSCh. 2 - A/B testing allows business to test a new design...Ch. 2 - Referring to the results from Problem 2.100 on...
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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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