assignment3solutions.pdf - Assignment 3 Solutions Include all answers to homework questions in one document and submit it online under Assignment 3

assignment3solutions.pdf - Assignment 3 Solutions Include...

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Assignment 3 Solutions Include all answers to homework questions in one document and submit it online under Assignment 3. Textbook Homework Questions From the OpenIntro textbook (Diez, Barr, and Çetinkaya-Rundel 2015), do the following questions: 2.10, 2.16, 2.22, 2.32, 2.38 . In addition, use R to answer the questions below. 2.10 Guessing on an Exam a) 0 . 75 4 * 0 . 25 = 0 . 079 b) 0 . 25 5 = 0 . 00098 c) 1 - 0 . 75 5 = 0 . 76 2.16 PB & J P ( likes jelly | likes peanut butter ) = P ( likes peanut butter AND likes jelly ) /P ( likes peanut butter ) = 0 . 78 / 0 . 8 = 0 . 975 2.22 Predisposition for Thrombosis We use Bayes’ Rule for this problem. What we know: P ( predisposition ) = 0 . 03 P ( positive | predisposition ) = 0 . 99 P ( negative | no predisposition ) = 0 . 98 So, using Bayes’ Rule: P ( predisposition | positive ) = P ( positive | predisposition ) P ( predisposition ) P ( positive ) = P ( positive | predisposition ) P ( predisposition ) P ( positive AND disposition )+ P ( positive AND no disposition ) = 0 . 99 * 0 . 03 0 . 99 * 0 . 03+0 . 02 * 0 . 97 = 0 . 60 2.32 The birthday problem a) 1 / 365 b) 1 - (364 / 365) * (363 / 365) = 0 . 0082 2.38 Baggage fees a) Bags 0 1 2 Value $0 $25 $35 Probability 0.54 0.34 0.12 1
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μ = 0 * 0 . 54 + 0 . 34 * 25 + 0 . 12 * 60 = 15 . 7 σ = (0 - 15 . 7) 2 * 0 . 54 + (25
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