Probability and Baye's Rule

Complete the following exercises. Show your work. You may either submit through blackboard, or submit a neatly-written paper copy before the deadline.

• Appendix A, problems 4-6.
• In class, we discussed a simple robot with a room sensor. What is the final probability distribution over room locations given the following series of sensor readings:
  
  b
  a
  b
  
  Assume that the initial distribution is uniform, the robot is not moving, and that sensor readings are independent given the robot's position. (I.e. one incorrect sensor reading does not increase the probability of seeing the same incorrect sensor reading in the future.)