HOMEWORK #8 Below, I give you multiple problems all based on a single probabilistic graphical model. P(N=Yes) P(N=No) 0.8 0.2 P(S=Yes) P(S=No) Party Last Night (N) 0.1 0.9 Sick (S) Hangover (H) N P(H=Yes) P(H=No) Exam Result (E) Yes 0.9 0.1 No 0.8 0.2 S H P(E=Good) P(E=Bad) V Y 0.1 0.9 N 0.5 0.5 N Y 0.6 0.4 N N 0.7 0.3 (1) Compute P(E=Good) (2) Compute P(S=Yes, H=Yes) (3) Compute P(N=No, S=Yes, H=No, E=Good) (4) Compute P(E=Good | N=Yes) (5) Compute P(E=Bad | S=No) Suppose Good exam result (E=Good) indicates exam scores higher than 70 points (out of 100). Your friend wanted to play a game with you. The rule is simple. If you get more than 70 from the exam tomorrow, your friend will give you $100. Otherwise, you have to give your friend $50. You know that there is no party tonight