Stats: Data And Models Plus Mylab Statistics With Pearson Etext -- Access Card Package (5th Edition)
5th Edition
ISBN: 9780135256213
Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock
Publisher: PEARSON
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Chapter 12, Problem 50E
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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 12 Solutions
Stats: Data And Models Plus Mylab Statistics With Pearson Etext -- Access Card Package (5th Edition)
Ch. 12.1 - JUST CHECKING
1. One common proposal for beating...Ch. 12.3 - Prob. 2JCCh. 12 - Prob. 1ECh. 12 - Prob. 2ECh. 12 - Prob. 3ECh. 12 - Prob. 4ECh. 12 - 5. Wardrobe In your dresser are five blue shirts,...Ch. 12 - 6. Playlists Your list of favorite songs contains...Ch. 12 - Prob. 7ECh. 12 - Cell phones and surveys II The survey by the...
Ch. 12 - Prob. 9ECh. 12 - 24. Sample spaces II For each of the following,...Ch. 12 - Prob. 11ECh. 12 - Prob. 12ECh. 12 - Prob. 13ECh. 12 - 28. Snow After an unusually dry autumn, a radio...Ch. 12 - Prob. 15ECh. 12 - Prob. 16ECh. 12 - 29. Auto insurance Insurance companies collect...Ch. 12 - Prob. 18ECh. 12 - Prob. 19ECh. 12 - Prob. 20ECh. 12 - Prob. 21ECh. 12 - 34. Homes Funding for many schools comes from...Ch. 12 - Prob. 23ECh. 12 - 36. Lefties Although it’s hard to be definitive in...Ch. 12 - Prob. 25ECh. 12 - Prob. 26ECh. 12 - Prob. 27ECh. 12 - 40. Stats projects In a large Introductory...Ch. 12 - More repairs Consider again the auto repair rates...Ch. 12 - Prob. 30ECh. 12 - Repairs again You used the Multiplication Rule to...Ch. 12 - Prob. 32ECh. 12 - Prob. 33ECh. 12 - Prob. 34ECh. 12 - More energy Exercise 33 shows the results of a...Ch. 12 - Prob. 36ECh. 12 - Prob. 37ECh. 12 - 46. Polling, part II According to Pew Research,...Ch. 12 - Prob. 39ECh. 12 - 48. Blood The American Red Cross says that about...Ch. 12 - Prob. 41ECh. 12 - Prob. 42ECh. 12 - Prob. 43ECh. 12 - Slot machine A slot machine has three wheels that...Ch. 12 - Prob. 45ECh. 12 - 52. The train To get to work, a commuter must...Ch. 12 - Prob. 47ECh. 12 - Religion Census reports for a city indicate that...Ch. 12 - Prob. 49ECh. 12 - 54. Pepsi For a sales promotion, the manufacturer...Ch. 12 - Prob. 51ECh. 12 - Prob. 52E
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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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