Basic Business Statistics
14th Edition
ISBN: 9780134684840
Author: BERENSON, Mark L., Levine, David M., Szabat, Kathryn A.
Publisher: Pearson,
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Chapter 1, Problem 19PS
Given a population of
a. without replacement.
b. with replacement.
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5. Let X and Y be independent random variables and let the superscripts denote
symmetrization (recall Sect. 3.6). Show that
(X + Y) X+ys.
8. Suppose that the moments of the random variable X are constant, that is, suppose
that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.
9. The concentration function of a random variable X is defined as
Qx(h) = sup P(x ≤ X ≤x+h), h>0.
Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qr (h)).
Chapter 1 Solutions
Basic Business Statistics
Ch. 1 - Four different beverages are sold at a fast-food...Ch. 1 - U. S. businesses are listed by size small medium,...Ch. 1 - The time it takes to download a video from the...Ch. 1 - For each of the following variables, determine...Ch. 1 - The following information is collected from...Ch. 1 - For each of the following variables, determine...Ch. 1 - For each of the following variables, determine...Ch. 1 - Suppose the following information is collected...Ch. 1 - One of the variables most often included in...Ch. 1 - If two students score a 90 on the same...
Ch. 1 - The director of market research at a large...Ch. 1 - The American Community Survey (www.census.gov/acs)...Ch. 1 - Visit the website of the Pew Research organization...Ch. 1 - Transportation engineers and planners want to...Ch. 1 - Visit the home page of the Statistics Portal...Ch. 1 - For a population containing N=902 individual, what...Ch. 1 - For a population of N=902, verify that by starting...Ch. 1 - Given a population of N=93, starting in row 29,...Ch. 1 - For a study that consists of personal interviews...Ch. 1 - You want to select a random sample of n=1 from a...Ch. 1 - A population has four members (called A, B, C, and...Ch. 1 - The registrar of a university with a population of...Ch. 1 - Prenumbered sales invoices are kept in a sales...Ch. 1 - Suppose that 10,000 customers in a retailer s...Ch. 1 - The cellphone brands owned by a sample of 20...Ch. 1 - The amount of monthly data usage by a sample of 10...Ch. 1 - An amusement park company owns three hotels on an...Ch. 1 - A hotel management company runs 10 hotels in a...Ch. 1 - A Survey indicates that the vast majority of...Ch. 1 - A simple random sample of n=300 full–time...Ch. 1 - Results of a 2017 Computer Service, Inc (CSI)...Ch. 1 - A recent PWC survey of 1,379 CEO s from a wide...Ch. 1 - A recent survey points to tremendous revenue...Ch. 1 - What is the difference between a sample and a...Ch. 1 - What is the difference between a statistic and...Ch. 1 - What is the difference between a categorical...Ch. 1 - What is the difference between a discrete...Ch. 1 - What is the difference between a nominal scaled...Ch. 1 - What is difference between an interval scaled...Ch. 1 - What is the difference between probability...Ch. 1 - What is difference between a missing value and an...Ch. 1 - What is the difference between unstack and stacked...Ch. 1 - What is the difference between coverage error and...Ch. 1 - What is the difference between sampling error and...Ch. 1 - Visit the official website for Microsoft Excel,...Ch. 1 - Results of a 2017 Computer Services, Inc (CSI)...Ch. 1 - The Gallup organization releases the results of...Ch. 1 - A recent PwC survey of 1,379 CEOs from a wide...Ch. 1 - The American community Survey (www.census.gov/acs)...Ch. 1 - Download and examine Zarca interactive’s Sample...Ch. 1 - Three professors examined awareness of four widely...Ch. 1 - Social media provides an enormous amount of data...
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- 10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward
- 7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward
- 1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x≤x≤x+h), h>0. = x (a) Show that Qx+b(h) = Qx(h).arrow_forwardSuppose that you buy a lottery ticket, and you have to pick six numbers from 1 through 50 (repetitions allowed). Which combination is more likely to win: 13, 48, 17, 22, 6, 39 or 1, 2, 3, 4, 5, 6? barrow_forward
- 2 Make a histogram from this data set of test scores: 72, 79, 81, 80, 63, 62, 89, 99, 50, 78, 87, 97, 55, 69, 97, 87, 88, 99, 76, 78, 65, 77, 88, 90, and 81. Would a pie chart be appropriate for this data? ganizing Quantitative Data: Charts and Graphs 45arrow_forward10 Meteorologists use computer models to predict when and where a hurricane will hit shore. Suppose they predict that hurricane Stat has a 20 percent chance of hitting the East Coast. a. On what info are the meteorologists basing this prediction? b. Why is this prediction harder to make than your chance of getting a head on your next coin toss? U anoiaarrow_forward6. Show that one cannot find independent, identically distributed random variables X and Y such that X-YE U(-1, 1). 7 Consider al onarrow_forward
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