Psychology 458/558<br>
Judgment and Decision Making<br>
Prof. Bertram Malle<br>
Fall 1995<P>
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<center><font size = 6> Assignments for conditional probabilities and
signal detection theory
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<b>If you turn in the solutions to these problems by Tuesday, Nov 14, you
can earn extra credit: 1 point for each correct solution and
an additional  point if both solutions are complete and perfect.</b>
<p>

<b>1.</b>  Suppose that
1 out of 10,000 doctors in a certain region is infected with AIDS virus.  A
test for the virus has been developed.  According to previous studies, the test
gives a positive result in 99% of those people who are infected and in 1% of
those who are not infected.  A randomly selected doctor in this region is
tested and gets a positive result.  What is the probability that this doctor is
infected? (Use both a 2x2 table and Bayes' theorem to solve this problem.)<p>
<p>
<p>
<b>2.</b>  Calculate the expected values of cutoff criteria I through III for
the two payoff matrices B and C (handout for lecture 9).  For each matrix,
answer the following questions:<p>
<p>
<ul>
<li>Which criterion is the best?  
<li>Why is this particular criterion the best?</ul>
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<b>Situation B</b><p>
<b></b>EV(I) = <br>
EV(II) = <br>
EV(III) = 
<p>
<b>Situation C</b><p>
<b></b>EV(I) = <br>
EV(II) = <br>
EV(III) = <p>
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