Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
7th Edition
ISBN: 9780134705187
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Chapter P, Problem 4DQ
Quantitative Literature. Choose a favorite work of literature (poem, play, short story. or novel). Describe one or more instances in which quantitative reasoning is helpful in understanding the subtleties intended by the author.
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2. Triple Integral Applications
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Find the volume of the solids in the first octant which bounded by xy-plane, yz-plane, plane
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2b.
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(b) An otherwise fair six-sided die has been tampered with in an attempt to
cheat at a dice game. The effect is that the 1 and 6 faces have a
different probability of occurring than the 2, 3, 4 and 5 faces.
Let θ be the probability of obtaining a 1 on this biased die. Then the
outcomes of rolling the biased die have the following probability mass
function.
Table 1 The p.m.f. of outcomes of rolls of a biased die
Outcome 1 2 3 4 5 6
Probability θ
1
4
(1 − 2θ)
1
4
(1 − 2θ)
1
4
(1 − 2θ)
1
4
(1 − 2θ) θ
(i) By consideration of the p.m.f. in Table 1, explain why it is
necessary for θ to be such that 0 < θ < 1/2. [2]
(ii) The value of θ is unknown. Data from which to estimate the value
of θ were obtained by rolling the biased die 1000 times. The result
of this experiment is shown in Table 2.
Table 2 Outcomes of 1000 independent rolls of a biased die
Outcome 1 2 3 4 5 6
Frequency 205 154 141 165 145 190
Show that the likelihood of θ based on these data is
L(θ) = C θ395 (1 − 2θ)
605
,…
Chapter P Solutions
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
Ch. P - Prob. 1DQCh. P - Quantitative Concepts in the News. Identify the...Ch. P - Mathematics and the Arts. Choose a well-known...Ch. P - Quantitative Literature. Choose a favorite work of...Ch. P - Your Quantitative Major. Identify ways in which...Ch. P - Career Preparation. Realizing that Americans...Ch. P - Attitudes Toward Mathematics. What is your...Ch. P - "Bad at Math" as a Social Disease. Discuss reasons...
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