We will use the Bayes filter to track the state It E IR of a robot. The prior probability density mction over the robot state at time t = D is 19(3) 2 Are"1 for :1: E [0, so) and 0 otherwise. The motion model is n+1 = on for or > 0. The robot is equipped with a sensor that provides observations according to the obscuration model at = if, where the measurement noise v: is independent of x; and has a probability density function q(v} = tie'3" for v E [0, so} and 0 otherwise. Assume that the robot observes before moving. {a} [9 pts] What is the nonlinear function h and the associated probability density function pm that describe the observation model? (b) [9 pts] What is the probability density function of the robot state 33.3 conditioned on the rst mea- surement so? (0] [9 ptsl What is the nonlinear function f and the associated probability density function Pf that describe the motion model? (d) [9 ptsl What is the probability density function of the robot state 2:1 (after moving) conditioned on the rst measurement an