Loose-leaf For Applied Statistics In Business And Economics
Loose-leaf For Applied Statistics In Business And Economics
5th Edition
ISBN: 9781259328527
Author: David Doane, Lori Seward Senior Instructor of Operations Management
Publisher: McGraw-Hill Education
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Chapter 1.3, Problem 1SE

Give an example of how statistics might be useful to the person in the scenario.

  1. a. An auditor is looking for inflated broker commissions in stock transactions.
  2. b. An industrial marketer is representing her firm’s compact, new low-power OLED screens to the military.
  3. c. A plant manager is studying absenteeism at vehicle assembly plants in three states.
  4. d. An automotive purchasing agent is comparing defect rates in steel shipments from three vendors of steel.
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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).

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Loose-leaf For Applied Statistics In Business And Economics

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