STA 301 - HW05 Key

STA 301 - HW05 Key - STA 301 Applied Statistics Spring...

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( 29 ( 29 ( 29 ( 29 05 . , 01 . | , 1 . | , 9 . | = = = = G P G T P G T P G T P ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1743 . 0545 . 0095 . 05 . * 9 . 95 . * 01 . 95 . * 01 . | | | | = + = + = = G P G T P G P G T P G P G T P T P T G P T G P I ( 29 = = = = 0 , 1 , 2 , 25 16 25 8 25 1 x x x x f STA 301 – Applied Statistics Spring 2008, Section B Homework #5 - Key Due Friday, February 29 Question 1 : (p. 73, #2.109) A truth serum has the property that 90% of the guilty suspects are properly judged while, of course, 10% of guilty suspects are improperly found innocent. On the other hand, innocent suspects are misjudged 1% of the time. If a suspect is selected from a group of people of whom only 5% have ever committed a crime, and the serum indicates that he is guilty, what is the probability that he is innocent? Define G = “guilty” and T = “tests guilty”. Then from the description of the problem, we have: Using Bayes’ Rule, we obtain
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STA 301 - HW05 Key - STA 301 Applied Statistics Spring...

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