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 52E
a.
To determine
Explain whether the thinking that there is a higher probability that the next card will be black than red is correct or not.
b.
To determine
Explain whether it is an example of Law of Large numbers or not.
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9. 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).
(b) Is it true that Qx(ah) =aQx(h)?
(c) Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qy (h)).
To put the concept in perspective, if X1, X2, X, are independent, identically
distributed random variables, and S₁ = Z=1Xk, then there exists an absolute
constant, A, such that
A
Qs, (h) ≤
√n
Some references: [79, 80, 162, 222], and [204], Sect. 1.5.
29
Suppose that a mound-shaped data set has a
must mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 6 and 12?
b. About what percentage of the data should
lie between 4 and 6?
c. About what percentage of the data should
lie below 4?
91002 175/1
3
2,3,
ample
and
rical
t?
the
28 Suppose that a mound-shaped data set has a
mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 8 and 12?
b. About what percentage of the data should
lie above 10?
c. About what percentage of the data should
lie above 12?
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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- 27 Suppose that you have a data set of 1, 2, 2, 3, 3, 3, 4, 4, 5, and you assume that this sample represents a population. The mean is 3 and g the standard deviation is 1.225.10 a. Explain why you can apply the empirical rule to this data set. b. Where would "most of the values" in the population fall, based on this data set?arrow_forward30 Explain how you can use the empirical rule to find out whether a data set is mound- shaped, using only the values of the data themselves (no histogram available).arrow_forward5. Let X be a positive random variable with finite variance, and let A = (0, 1). Prove that P(X AEX) 2 (1-A)² (EX)² EX2arrow_forward
- 6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows: P(X=-x) = P(X = x)=p. P(X=0)= 1-2p. Show that there is equality in Chebyshev's inequality for X. This means that Chebyshev's inequality, in spite of being rather crude, cannot be improved without additional assumptions.arrow_forward4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined as a product of independent, identically distributed random variables with mean 1 (under the so-called null hypothesis), and the, sometimes more convenient, log-likelihood, log L, which was a sum of independent, identically distributed random variables, which, however, do not have mean log 1 = 0. (a) Verify that the last claim is correct, by proving the more general statement, namely that, if Y is a non-negative random variable with finite mean, then E(log Y) log(EY). (b) Prove that, in fact, there is strict inequality: E(log Y) < log(EY), unless Y is degenerate. (c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a glimpse on (b).arrow_forward
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