ELEMENTARY STATISTICS USING EXCEL
7th Edition
ISBN: 9780136921721
Author: Triola
Publisher: RENT PEARS
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Chapter 6.1, Problem 17BSC
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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.
4. Prove that, for any random variable X, the minimum of EIX-al is attained for
a = med (X).
8. 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).
Chapter 6 Solutions
ELEMENTARY STATISTICS USING EXCEL
Ch. 6.1 - 1. Normal Distribution What’s wrong with the...Ch. 6.1 - Prob. 2BSCCh. 6.1 - Prob. 3BSCCh. 6.1 - Prob. 4BSCCh. 6.1 - Continuous Uniform Distribution. In Exercises 5–8,...Ch. 6.1 - Continuous Uniform Distribution. In Exercises 5–8,...Ch. 6.1 - Prob. 7BSCCh. 6.1 - Prob. 8BSCCh. 6.1 - Standard Normal Distribution. In Exercises 9–12,...Ch. 6.1 - Standard Normal Distribution. In Exercises 9–12,...
Ch. 6.1 - Standard Normal Distribution. In Exercises 9–12,...Ch. 6.1 - Standard Normal Distribution. In Exercises 9–12,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Prob. 17BSCCh. 6.1 - Prob. 18BSCCh. 6.1 - Prob. 19BSCCh. 6.1 - Prob. 20BSCCh. 6.1 - Prob. 21BSCCh. 6.1 - Prob. 22BSCCh. 6.1 - Prob. 23BSCCh. 6.1 - Prob. 24BSCCh. 6.1 - Prob. 25BSCCh. 6.1 - Prob. 26BSCCh. 6.1 - Prob. 27BSCCh. 6.1 - Prob. 28BSCCh. 6.1 - Prob. 29BSCCh. 6.1 - Prob. 30BSCCh. 6.1 - Prob. 31BSCCh. 6.1 - Prob. 32BSCCh. 6.1 - Prob. 33BSCCh. 6.1 - Prob. 34BSCCh. 6.1 - Prob. 35BSCCh. 6.1 - Prob. 36BSCCh. 6.1 - Finding Bone Density Scores. In Exercises 37–40...Ch. 6.1 - Prob. 38BSCCh. 6.1 - Prob. 39BSCCh. 6.1 - Prob. 40BSCCh. 6.1 - Prob. 41BSCCh. 6.1 - Prob. 42BSCCh. 6.1 - Prob. 43BSCCh. 6.1 - Prob. 44BSCCh. 6.1 - Prob. 45BSCCh. 6.1 - Prob. 46BSCCh. 6.1 - Prob. 47BSCCh. 6.1 - Prob. 48BSCCh. 6.1 - Prob. 49BBCh. 6.1 - Prob. 50BBCh. 6.2 - Prob. 1BSCCh. 6.2 - Prob. 2BSCCh. 6.2 - Prob. 3BSCCh. 6.2 - Prob. 4BSCCh. 6.2 - IQ Scores. In Exercises 5–8, find the area of the...Ch. 6.2 - IQ Scores. In Exercises 5–8, find the area of the...Ch. 6.2 - Prob. 7BSCCh. 6.2 - IQ Scores. In Exercises 5–8, find the area of the...Ch. 6.2 - IQ Scores. In Exercises 9–12, find the indicated...Ch. 6.2 - IQ Scores. In Exercises 9–12, find the indicated...Ch. 6.2 - Prob. 11BSCCh. 6.2 - Prob. 12BSCCh. 6.2 - Prob. 13BSCCh. 6.2 - Prob. 14BSCCh. 6.2 - Prob. 15BSCCh. 6.2 - Prob. 16BSCCh. 6.2 - Prob. 17BSCCh. 6.2 - Prob. 18BSCCh. 6.2 - Prob. 19BSCCh. 6.2 - Prob. 20BSCCh. 6.2 - Prob. 21BSCCh. 6.2 - Prob. 22BSCCh. 6.2 - Prob. 23BSCCh. 6.2 - Prob. 24BSCCh. 6.2 - Prob. 25BSCCh. 6.2 - In Exercises 21–24, use these parameters (based on...Ch. 6.2 - In Exercises 21–24, use these parameters (based on...Ch. 6.2 - Prob. 28BSCCh. 6.2 - Prob. 29BSCCh. 6.2 - Prob. 30BSCCh. 6.2 - Prob. 31BSCCh. 6.2 - Prob. 32BSCCh. 6.2 - Prob. 33BSCCh. 6.2 - Prob. 34BSCCh. 6.2 - Prob. 35BSCCh. 6.2 - Prob. 36BSCCh. 6.2 - Prob. 37BBCh. 6.2 - Prob. 38BBCh. 6.3 - Prob. 1BSCCh. 6.3 - Prob. 2BSCCh. 6.3 - Prob. 3BSCCh. 6.3 - Prob. 4BSCCh. 6.3 - Prob. 5BSCCh. 6.3 - Prob. 6BSCCh. 6.3 - Prob. 7BSCCh. 6.3 - Prob. 8BSCCh. 6.3 - Prob. 9BSCCh. 6.3 - In Exercises 7–10, use the same population of {4,...Ch. 6.3 - Prob. 11BSCCh. 6.3 - Prob. 12BSCCh. 6.3 - Prob. 13BSCCh. 6.3 - Prob. 14BSCCh. 6.3 - Prob. 15BSCCh. 6.3 - Prob. 16BSCCh. 6.3 - Prob. 17BSCCh. 6.3 - Prob. 18BSCCh. 6.3 - Prob. 19BBCh. 6.3 - Prob. 20BBCh. 6.4 - Prob. 1BSCCh. 6.4 - Prob. 2BSCCh. 6.4 - Prob. 3BSCCh. 6.4 - Prob. 4BSCCh. 6.4 - Prob. 5BSCCh. 6.4 - Prob. 6BSCCh. 6.4 - Prob. 7BSCCh. 6.4 - Prob. 8BSCCh. 6.4 - Prob. 9BSCCh. 6.4 - Prob. 10BSCCh. 6.4 - Prob. 11BSCCh. 6.4 - Prob. 12BSCCh. 6.4 - Prob. 13BSCCh. 6.4 - Prob. 14BSCCh. 6.4 - Prob. 15BSCCh. 6.4 - Prob. 16BSCCh. 6.4 - Prob. 17BSCCh. 6.4 - Prob. 18BSCCh. 6.4 - Prob. 19BSCCh. 6.4 - Prob. 20BBCh. 6.5 - Prob. 1BSCCh. 6.5 - Prob. 2BSCCh. 6.5 - Prob. 3BSCCh. 6.5 - Prob. 4BSCCh. 6.5 - Prob. 5BSCCh. 6.5 - Prob. 6BSCCh. 6.5 - Prob. 7BSCCh. 6.5 - Prob. 8BSCCh. 6.5 - Prob. 9BSCCh. 6.5 - Prob. 10BSCCh. 6.5 - Prob. 11BSCCh. 6.5 - Prob. 12BSCCh. 6.5 - Prob. 13BSCCh. 6.5 - Prob. 14BSCCh. 6.5 - Prob. 15BSCCh. 6.5 - Prob. 16BSCCh. 6.5 - Prob. 17BSCCh. 6.5 - Prob. 18BSCCh. 6.5 - Prob. 19BSCCh. 6.5 - Prob. 20BSCCh. 6.5 - Prob. 21BBCh. 6.5 - Prob. 22BBCh. 6 - Prob. 1CQQCh. 6 - Prob. 2CQQCh. 6 - Prob. 3CQQCh. 6 - Prob. 4CQQCh. 6 - Prob. 5CQQCh. 6 - Prob. 6CQQCh. 6 - Prob. 7CQQCh. 6 - Prob. 8CQQCh. 6 - Prob. 9CQQCh. 6 - Prob. 10CQQCh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 1CRECh. 6 - Prob. 2CRECh. 6 - Prob. 3CRECh. 6 - Prob. 4CRECh. 6 - Prob. 5CRECh. 6 - Prob. 1FDD
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