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