6. (10 points) You are still strying to find your friend in the building (from MT3). F1 is the first floor and F4 is the fourth floor. Your friend randomly moves between the floors. The probability of going up and down by one level at each floor (e.g. your friend can only go to 1st or 3rd floor, or stay in the 2nd floor if he is already in the 2nd floor) is given below. In addition, there is a sound sensor on the first floor with emission probabilities given below. XT Stay Down Up d: floor difference F4 F4 0.6 0.4 S P(S|X) from the first floor F3 X = F1, d=0 F3 0.5 0.3 0.2 -S 0.1+0.2d F2 X = F2, d=1 F2 0.5 0.2 0.3 +S 0.9-0.2d X = F3, d=2 F1 F1 0.6 0.4 X = F4, d=3 This time you are going to use particle filtering to try to find your friend. (a) (2 points) The sensor senses a sound (S=+s). What is the weight of each particle for a given state after this observation? Show your work below the table and fill the table with your results F1 F2 F3 F4