CISC 7700X Final Exam

1. c
2. d, https://en.wikipedia.org/wiki/Raven_paradox
3. b, % we found a random widget, there is a 50% chance that the serial number 54321 is within the interquartile range of all serial numbers.
4. b
5. a 
6. 5%, it's right in the question: ``About 5% of those that have symptoms end up testing positive.''
7. b
8. c
9. d
10. 0.51429
% D=defalt, M=mustache, P(D) = 0.15, P(-D) = 0.85, P(M|D)=0.6, P(-M|D)=0.4, P(M|-D)=0.1, P(-M|-D)=0.9,
% P(D|M) = P(M|D)P(D) / (P(M|D)P(D)+P(M|-D)P(-D)) = (0.6*0.15)/((0.6*0.15)+(0.1*0.85)) = 0.51429
% check: P(-D|M) = P(M|-D)*P(-D) / (P(M|-D)*P(-D)+P(M|D)*P(D)) = (0.1*0.85)/((0.1*0.85)+(0.6*0.15))=0.48571
11. c
12. 0.091603
% D=default, P(D) = 0.15, P(-D) = 0.85, P(40-100k|D)=0.2, P(40-100k|-D)=0.35,
% P(D|50K)=P(D|40-100k)=P(40-100k|D)P(D)/(P(40-100k|D)P(D)+P(40-100k|-D)P(-D))=(0.2*0.15)/((0.2*0.15)+(0.35*0.85))=0.091603
13. 0.38849
% C=car-loan, P(D) = 0.15, P(-D) = 0.85, P(C|D)=0.9, P(C|-D)=0.25 
% P(D|C) = P(C|D)P(D)/(P(C|D)P(D)+P(C|-D)P(-D))= (0.9*0.15)/((0.9*0.15)+(0.25*0.85))=0.38849
14. Not enough information: the income bracket and existence of a car loan may not be independent.
15. 0.26634
% D=default, C=car-loan, P(D|50K)=0.091603,  P(-D|50K)=(1-0.091603), P(C|D)=0.9, P(C|-D)=0.25
% P(D|C)=P(C|D)P(D|50K)/(P(C|D)P(D|50K)+P(C|-D)P(-D|50K))=(0.9*0.091603)/((0.9*0.091603)+(0.25*(1-0.091603)))=0.26634
% check:  P(D|C) = 0.38849, P(-D|C)=(1-0.38849), P(50k|D)=0.2, P(50k|-D)=0.35
% P(D|50K)=P(50K|D)P(D|C)/(P(50K|D)P(D|C)+P(50K|-D)P(-D|C))=(0.2*0.38849)/((0.2*0.38849)+(0.35*(1-0.38849)))=0.26634
16. b
17. d
18. 1.00
19. 0.75
20. 0.64952, % exp( 3*( 0.5*log(1+0.5)+0.5*log(1-0.5)) )

All outcomes: 

1.0 * (1-0.5)* (1-0.5)* (1-0.5) = 0.125
1.0 * (1+0.5)* (1-0.5)* (1-0.5) = 0.375
1.0 * (1-0.5)* (1+0.5)* (1-0.5) = 0.375
1.0 * (1+0.5)* (1+0.5)* (1-0.5) = 1.125
1.0 * (1-0.5)* (1-0.5)* (1+0.5) = 0.375
1.0 * (1+0.5)* (1-0.5)* (1+0.5) = 1.125
1.0 * (1-0.5)* (1+0.5)* (1+0.5) = 1.125
1.0 * (1+0.5)* (1+0.5)* (1+0.5) = 3.375
0.125,0.375,0.375,0.375,1.125,1.125,1.125,3.375
median: (0.375+1.125)/2.0 = 0.75
arith mean: 1
geom mean: 0.649519052838329