A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

13th Edition

ISBN: 9780135183885

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott, Barbara Boschmans

Publisher: PEARSON

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Chapter 2.2B, Problem 14A

Indicate which symbol, ∈ or ∉ , makes each of the following statements true.

a. ∅ _______ { ∅ }

b. 1022______ { s | s = 2 n − 2 and n ∈ N }

c. 3004______ { x | x = 3 n + 1 and n ∈ N }

d. 17________N

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Chapter 2.2B, Problem 13A

Chapter 2.2B, Problem 15A

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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 2 Solutions

A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

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Indicate which symbol, ∈ or ∉ , makes each of the following statements true. a. ∅ _______ { ∅ } b. 1022______ { s | s = 2 n − 2 and n ∈ N } c. 3004______ { x | x = 3 n + 1 and n ∈ N } d. 17________ N

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Chapter 2 Solutions

Indicate which symbol, ∈ or ∉ , makes each of the following statements true. a. ∅ _ { ∅ } b. 1022 { s | s = 2 n − 2 and n ∈ N } c. 3004 { x | x = 3 n + 1 and n ∈ N } d. 17__ N