CISC 7700X Final Exam

1. c
2. b
3. c
4. e
5. b
6. b
7. a
8. c
9. e: 20/21 or 0.9523 or 0.95 or 95%, full answer below
10. c
11. a, full answer below
12. e: 9/17 or 0.5294 or 0.53 or 53%, full answer below
13. d
14. e: 9/25 or 0.36 or 36%, full answer below
15: b
16: e
17: b
18: b
19: c
20: d


9: from question: d=default, m=mustache, 
 p(d)=1/5, p(-d)=4/5
 p(m|d)=4/5, p(m|-d)=1/100
 We use bayes rule: p(d|m)= p(m|d)p(d) / (p(m|d)p(d)+p(m|-d)p(-d))
  4/5*1/5 / ( 4/5*1/5 + 1/100*4/5 ) = 20/21

11: from question: d=default, 
 p(d)=1/5, p(-d)=4/5
 p(40-100k|d)=1/5, p(40-100k|-d)=2/5
 We use bayes rule: p(d|40-100k)= p(40-100k|d)p(d) / (p(40-100k|d)p(d)+p(40-100k|-d)p(-d))
  1/5*1/5 / (1/5*1/5 + 2/5*4/5) = 1/9

12. from question: d=default, c=car-loan
 p(d)=1/5, p(-d)=4/5
 p(c|d)=9/10, p(c|-d)=1/5
 We use bayes rule: p(d|c) = p(c|d)p(d) / (p(c|d)p(d) + p(c|-d)p(-d))
  9/10*1/5 / (9/10*1/5 + 1/5*4/5) = 9/17

14: from question: d=default, c=car-loan, 
 p(d) = p(d|40-100k) = 1/9, p(-d) = p(-d|40-100k) = 8/9
 p(c|d)=9/10, p(c|-d)=1/5
 We use bayes rule: p(d|c) = p(c|d)p(d) / (p(c|d)p(d) + p(c|-d)p(-d))
  9/10*1/9 / (9/10*1/9 + 1/5*8/9) = 9/90 / (9/90 + 16/90) = 9/90 / 25/90 = 9/25 
 ---can also do this the other way around (first car-loan, then income bracket)
 p(d) = p(d|c) = 9/17, p(-d) = p(-d|c) = 8/17
 p(40-100k|d) = 1/5, p(40-100k|-d) = 2/5
 We use bayes rule: p(d|40-100k)= p(40-100k|d)p(d) / (p(40-100k|d)p(d)+p(40-100k|-d)p(-d))
  1/5*9/17 / (1/5*9/17 + 2/5*8/17) = 9/85 / (9/85+16/85) = 9/85 / 25/85 = 9/25