diff --git a/tracking/inference.py b/tracking/inference.py
index 0c3ad9f..c1bb7e3 100644
--- a/tracking/inference.py
+++ b/tracking/inference.py
@@ -648,7 +648,10 @@ class ParticleFilter(InferenceModule):
         """
         self.particles = []
         "*** YOUR CODE HERE ***"
-        raiseNotDefined()
+        num_positions = len(self.legalPositions)
+        num_particles = self.numParticles
+        for i in range(num_particles):
+            self.particles.append(self.legalPositions[i % num_positions])
         "*** END YOUR CODE HERE ***"
 
     def getBeliefDistribution(self):
@@ -660,7 +663,11 @@ class ParticleFilter(InferenceModule):
         This function should return a normalized distribution.
         """
         "*** YOUR CODE HERE ***"
-        raiseNotDefined()
+        belief = DiscreteDistribution()
+        for particle in self.particles:
+            belief[particle] += 1
+        belief.normalize()
+        return belief
         "*** END YOUR CODE HERE ***"
     
     ########### ########### ###########
@@ -680,7 +687,14 @@ class ParticleFilter(InferenceModule):
         the DiscreteDistribution may be useful.
         """
         "*** YOUR CODE HERE ***"
-        raiseNotDefined()
+        belief = DiscreteDistribution()
+        for particle in self.particles:
+            belief[particle] += self.getObservationProb(observation, gameState.getPacmanPosition(), particle, self.getJailPosition())
+        belief.normalize()
+        if belief.total() == 0:
+            self.initializeUniformly(gameState)
+        else:
+            self.particles = [belief.sample() for _ in range(self.numParticles)]
         "*** END YOUR CODE HERE ***"
     
     ########### ########### ###########
@@ -693,6 +707,9 @@ class ParticleFilter(InferenceModule):
         gameState.
         """
         "*** YOUR CODE HERE ***"
-        raiseNotDefined()
+        new_particles = []
+        for particle in self.particles:
+            new_particles.append(self.getPositionDistribution(gameState, particle).sample())
+        self.particles = new_particles
         "*** END YOUR CODE HERE ***"