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Chapter 8: Q96SE (page 452)
For two events A and B, suppose ,,Find.
The value of is 0.8.
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Fingerprint expertise.A study published in PsychologicalScience(August 2011) tested the accuracy of experts andnovices in identifying fingerprints. Participants were presentedpairs of fingerprints and asked to judge whetherthe prints in each pair matched. The pairs were presentedunder three different conditions: prints from the same individual (match condition), non-matching but similar prints (similar distracter condition), and nonmatching and very dissimilar prints (non-similar distracter condition). The percentages of correct decisions made by the two groups under each of the three conditions are listed in the table.
Conditions | Fingerprints expert | Novices |
Match similar | 92.12% | 74.55% |
Distracter | 99.32% | 44.82% |
Non-similar distracter | 100% | 77.03% |
a.Given a pair of matched prints, what is the probability that an expert failed to identify the match?
b. Given a pair of matched prints, what is the probabilitythat a novice failed to identify the match?
c. Assume the study included 10 participants, 5 experts and 5 novices. Suppose that a pair of matched prints was presented to a randomly selected study participant and the participant failed to identify the match. Is the participant more likely to be an expert or a novice?
Forensic analysis of JFK assassination bullets. Following theassassination of President John F. Kennedy (JFK) in 1963, the House Select Committee on Assassinations (HSCA) conducted an official government investigation. The HSCA concluded that although there was a probable conspiracy involving at least one shooter in addition to Lee Harvey Oswald, the additional shooter missed all limousine occupants. A recent analysis of assassination bullet fragments, reported in the Annals of Applied Statistics(Vol. 1, 2007), contradicted these findings, concluding that the evidence used by the HSCA to rule out a second assassin is fundamentally flawed. It is well documented that at least two different bullets were the source of bullet fragments found after the assassination. Let E= {bullet evidence used by the HSCA}, T= {two bullets used in the assassination}, and= {more than two bullets used in the assassination}. Given the evidence (E), which is more likely to have occurred鈥� two bullets used (T) or more than two bullets used ?
a. The researchers demonstrated that the ratio,, is less than 1. Explain why this result supports the theory of more than two bullets used in the assassination of JFK.
b. To obtain the result, part a, the researchers first showed that Demonstrate this equality using Bayes鈥檚 Rule.
The 鈥渨inner鈥檚 curse鈥� in transaction bidding. In transaction bidding, the 鈥渨inner鈥檚 curse鈥� is the miracle of the winning (or loftiest) shot price being above the anticipated value of the item being auctioned. The Review of Economics and Statistics (Aug. 2001) published a study on whether shot experience impacts the liability of the winner鈥檚 curse being. Two groups of a stab in a sealed-shot transaction were compared (1)super-experienced stab and (2) less educated stab. In the super-experienced group, 29 of 189 winning flings were above the item鈥檚 anticipated value; 32 of 149 winning flings were above the item鈥檚 anticipated value in the less-educated group.
A random sample of n observations is selected from a normal population to test the null hypothesis that . Specify the rejection region for each of the following combinations of and .
a.
b.
c.
d.
e.
f.
4.135 Suppose xhas an exponential distribution with . Find
the following probabilities:
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