CISC 7700X Midterm Exam

1. b
2. c
3. b
4. d
5. d
6. 1000^11
 for(all values of A)
  for(all values of B)
   for(all values of C) ... etc.

7. 0.75

  all outcomes:
     0 wins: 0.125, e.g. $1 * 0.5 * 0.5 * 0.5
     1 wins: 0.375,0.375,0.375
     2 wins: 1.125,1.125,1.125
     3 wins: 3.375
  median is (0.375+1.125)/2 = 0.75

8. 0.649519

  eg. exp((log(0.125)+3*log(0.375)+3*log(1.125)+log(3.375))/8)

9. 1.

  all outcomes:
     0 wins: 0.125, e.g. $1 * 0.5 * 0.5 * 0.5
     1 wins: 0.375,0.375,0.375
     2 wins: 1.125,1.125,1.125
     3 wins: 3.375
  mean is (0.125 + 3*0.375 + 3*1.125 + 3.375)/8 = 1

10. c
11. c
12. d
13. b
14. e, identify, that' show conditional probability   is defined.
15. 0.4000

  Given: P(U) = 0.1, P(-U) = 0.9, P(F|U) = 0.6, P(F|-U) = 0.1
  P(U|F) = P(F|U)P(U) / P(F) 
         = P(F|U)P(U) / ( P(F|U)P(U) + P(F|-U)P(-U) )
         = (0.6*0.1) / (0.6*0.1 + 0.1*0.9) = 0.4000

16. 0.4706

  Given: P(U) = 0.1, P(-U) = 0.9, P(I|U) = 0.4, P(I|-U) = 0.05
  P(U|I) = P(I|U)P(U) / P(I)
         = P(I|U)P(U) / (P(I|U)P(U) + P(I|-U)P(-U))
         = (0.4*0.1) / (0.4*0.1 + 0.05*0.9) = 0.4706

17. P(U|F,I) = P(F,I|U)P(U) / P(F,I)
             = P(F,I|U)P(U) / (P(F,I|U)P(U) + P(F,I|-U)P(-U)) 
    Cannot calculate; we do not know P(F,I|U) and P(F,I). 

18. 0.8421

    P(U|F,I) = P(F|U)P(I|U)P(U) / P(F)P(I)
             = P(F|U)P(I|U)P(U) / (P(F|U)P(I|U)P(U) + P(F|-U)P(I|-U)P(-U))
             = (0.6*0.4*0.1) / (0.6*0.4*0.1 + 0.1*0.05*0.9) = 0.8421

19. what if nobody got vaccinated?

20. c