Elementary Statistics Using Excel (6th Edition)
6th Edition
ISBN: 9780134506623
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 4.1, Problem 36BSC
To determine
To obtain: The
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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 4 Solutions
Elementary Statistics Using Excel (6th Edition)
Ch. 4.1 - 1. New Jersey Lottery Let A denote the event of...Ch. 4.1 - 2. Probability Rewrite the following statement so...Ch. 4.1 - 3. Interpreting Weather While this exercise was...Ch. 4.1 - 4. Subjective Probability Estimate the probability...Ch. 4.1 - 5. Identifying Probability Values Which of the...Ch. 4.1 - 6. Penicillin “Who discovered penicillin: Sean...Ch. 4.1 - 7. Avogadro Constant If you are asked on a quiz to...Ch. 4.1 - 8. Births Example 2 in this section includes the...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...
Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - 14. SAT Test When making a random guess for an...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - 17. Randomness When using a computer to randomly...Ch. 4.1 - Prob. 18BSCCh. 4.1 - Prob. 19BSCCh. 4.1 - Prob. 20BSCCh. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - Prob. 27BSCCh. 4.1 - Prob. 28BSCCh. 4.1 - Prob. 29BSCCh. 4.1 - Prob. 30BSCCh. 4.1 - Prob. 31BSCCh. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - Prob. 33BSCCh. 4.1 - Prob. 34BSCCh. 4.1 - Prob. 35BSCCh. 4.1 - Prob. 36BSCCh. 4.1 - Prob. 37BSCCh. 4.1 - Prob. 38BSCCh. 4.1 - Prob. 39BSCCh. 4.1 - Prob. 40BSCCh. 4.1 - Prob. 41BBCh. 4.1 - Prob. 42BBCh. 4.1 - Prob. 43BBCh. 4.1 - Prob. 44BBCh. 4.2 - 1. Notation When randomly selecting an adult, A...Ch. 4.2 - 2. Notation When randomly selecting adults, let M...Ch. 4.2 - 3. Sample for a Poll There are 15,524,971 adults...Ch. 4.2 - Prob. 4BSCCh. 4.2 - Prob. 5BSCCh. 4.2 - Prob. 6BSCCh. 4.2 - Prob. 7BSCCh. 4.2 - Prob. 8BSCCh. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20; use the data in the following...Ch. 4.2 - Prob. 14BSCCh. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - Prob. 21BSCCh. 4.2 - Prob. 22BSCCh. 4.2 - Prob. 23BSCCh. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - Prob. 25BSCCh. 4.2 - Prob. 26BSCCh. 4.2 - Prob. 27BSCCh. 4.2 - Prob. 28BSCCh. 4.2 - Prob. 29BSCCh. 4.2 - Prob. 30BSCCh. 4.2 - Prob. 31BBCh. 4.2 - 32. Same Birthdays If 25 people are randomly...Ch. 4.2 - Prob. 33BBCh. 4.2 - Prob. 34BBCh. 4.3 - 1. Language: Complement of “At Least One” Let A =...Ch. 4.3 - 2. Probability of At Least One Let A = the event...Ch. 4.3 - 3. Notation When selecting one of your Facebook...Ch. 4.3 - 3. Notation When selecting one of your Facebook...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - 6. Probability of a Girl Assuming that boys and...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Prob. 11BSCCh. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Prob. 14BSCCh. 4.3 - Prob. 15BSCCh. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Prob. 17BSCCh. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - Prob. 19BSCCh. 4.3 - Prob. 20BSCCh. 4.3 - Prob. 21BSCCh. 4.3 - Prob. 22BSCCh. 4.3 - Prob. 23BSCCh. 4.3 - 24. Composite Water Samples The Fairfield County...Ch. 4.3 - Prob. 25BBCh. 4.4 - 1. Notation What does the symbol ! represent? Six...Ch. 4.4 - Prob. 2BSCCh. 4.4 - Prob. 3BSCCh. 4.4 - Prob. 4BSCCh. 4.4 - In Exercises 5–36, express all probabilities as...Ch. 4.4 - 6. Social Security Numbers A Social Security...Ch. 4.4 - Prob. 7BSCCh. 4.4 - 8. Soccer Shootout In soccer, a tie at the end of...Ch. 4.4 - 9. Grading Exams Your professor has just collected...Ch. 4.4 - 10. Radio Station Call Letters If radio station...Ch. 4.4 - 11. Scheduling Routes A presidential candidate...Ch. 4.4 - 12. Survey Reliability A survey with 12 questions...Ch. 4.4 - Prob. 13BSCCh. 4.4 - Prob. 14BSCCh. 4.4 - Prob. 15BSCCh. 4.4 - Prob. 16BSCCh. 4.4 - Prob. 17BSCCh. 4.4 - Prob. 18BSCCh. 4.4 - 19. ZIP Code If you randomly select five digits,...Ch. 4.4 - Prob. 20BSCCh. 4.4 - Prob. 21BSCCh. 4.4 - Prob. 22BSCCh. 4.4 - Prob. 23BSCCh. 4.4 - Prob. 24BSCCh. 4.4 - Prob. 25BSCCh. 4.4 - Prob. 26BSCCh. 4.4 - Prob. 27BSCCh. 4.4 - Prob. 28BSCCh. 4.4 - 29. Mega Millions As of this writing, the Mega...Ch. 4.4 - Prob. 30BSCCh. 4.4 - Prob. 31BSCCh. 4.4 - Prob. 32BSCCh. 4.4 - Prob. 33BSCCh. 4.4 - Prob. 34BSCCh. 4.4 - Prob. 35BSCCh. 4.4 - Prob. 36BSCCh. 4.4 - Prob. 37BBCh. 4.4 - Prob. 38BBCh. 4.5 - Simulating Dice When two dice are rolled, the...Ch. 4.5 - Prob. 2BSCCh. 4.5 - Prob. 3BSCCh. 4.5 - Prob. 4BSCCh. 4.5 - Prob. 5BSCCh. 4.5 - Prob. 6BSCCh. 4.5 - Prob. 7BSCCh. 4.5 - Prob. 8BSCCh. 4.5 - Prob. 9BSCCh. 4.5 - Prob. 10BSCCh. 4.5 - Prob. 11BSCCh. 4.5 - Prob. 12BSCCh. 4.5 - Prob. 13BSCCh. 4.5 - Prob. 14BSCCh. 4.5 - Prob. 15BSCCh. 4.5 - Prob. 16BSCCh. 4.5 - Prob. 17BBCh. 4.5 - Prob. 18BBCh. 4 - Prob. 1CQQCh. 4 - Prob. 2CQQCh. 4 - Prob. 3CQQCh. 4 - Prob. 4CQQCh. 4 - Prob. 5CQQCh. 4 - Prob. 6CQQCh. 4 - Prob. 7CQQCh. 4 - Prob. 8CQQCh. 4 - Prob. 9CQQCh. 4 - Prob. 10CQQCh. 4 - Prob. 1RECh. 4 - In Exercises 1–10, use the data in the...Ch. 4 - In Exercises 1–10, use the data in the...Ch. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 1CRECh. 4 - Prob. 2CRECh. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Prob. 5CRECh. 4 - Prob. 6CRECh. 4 - Prob. 1EPCh. 4 - Prob. 1FDDCh. 4 - Prob. 2FDDCh. 4 - Prob. 3FDDCh. 4 - Prob. 4FDDCh. 4 - Prob. 5FDDCh. 4 - Prob. 6FDDCh. 4 - Prob. 7FDDCh. 4 - Prob. 8FDDCh. 4 - Prob. 9FDD
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