Basic Business Statistics
14th Edition
ISBN: 9780134684840
Author: BERENSON, Mark L., Levine, David M., Szabat, Kathryn A.
Publisher: Pearson,
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Chapter 7, Problem 24PS
What is the difference between a population distribution and a sampling distribution?
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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 7 Solutions
Basic Business Statistics
Ch. 7 - Given a normal distribution with =100and=10, if...Ch. 7 - Given a normal distribution with =50and=5, if you...Ch. 7 - For each of the following three populations,...Ch. 7 - The following data represent the number of days...Ch. 7 - The amount of water in a two-liter bottle is...Ch. 7 - The weight of an energy bar is approximately...Ch. 7 - The diameter of a brand of tennis balls is...Ch. 7 - The U.S. Census Bureau announced that the median...Ch. 7 - According to a report by App Annie, a business...Ch. 7 - According to the National Survey of Student...
Ch. 7 - In a random sample of 64 people, 48 are classified...Ch. 7 - A random sample of 50 households was selected for...Ch. 7 - The following data represent the responses (Y for...Ch. 7 - A political pollster is conducting an analysis of...Ch. 7 - You plan to conduct a marketing experiment in...Ch. 7 - What do millennials around the world want in a...Ch. 7 - The goal of corporate sustainability is to manage...Ch. 7 - Prob. 18PSCh. 7 - The topic of global warming increasingly appears...Ch. 7 - An IAB study on the state of original digital...Ch. 7 - Why is the sample mean an unbiased estimator of...Ch. 7 - Why does the standard error of the mean decrease...Ch. 7 - Why does the sampling distribution of the mean...Ch. 7 - What is the difference between a population...Ch. 7 - Under what circumstances does the sampling...Ch. 7 - An industrial sewing machine uses ball bearings...Ch. 7 - The fill amount of bottles of a soft drinks is...Ch. 7 - Prob. 28PSCh. 7 - In problem 7.28, suppose that the mean amount of...Ch. 7 - Prob. 30PSCh. 7 - The article mentioned in Problem 7.30 reported...
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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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