hw7 - CSE 321 Discrete Structures Autumn 2008 Problems...

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CSE 321: Discrete Structures Assignment #7 Autumn 2008 Due: Monday, December 1 Problems: 1. When a test for steroids is given to soccer players, 98% of the players taking steroids test positive and 12% of the players not taking steroids test positive. Suppose that 5% of soccer players take steroids. What is the probability that a soccer player who tests positive takes steroids? 2. Mobile robot localization : Bayes’ rule underlies all modern AI systems for probabilistic inference. One application of this rule is the update of a robot’s position estimate based on new sensor information. To see, look at the example below. 0 1 2 3 4 The robot is placed in the hallway facing east and it does not know where it is (it only knows its orientation). The hallway is tessellated and the robot can be in any of the five squares (always facing east). Assume that the width of each square is 1 meter. Then the squares are numbered by their distance from the beginning of the hallway. Given the tessellation of the hallway, we can represent the position of the robot by a random variable L . This variable takes on values between 0 and 4, depending on the robot’s current position. At each point in time, the robot’s position estimate is represented by a probability distribution over all possible locations. In the beginning, the robot does not know where it is. This can be represented by the following distribution: P ( L = 0) = P ( L = 1) = P ( L = 2) = P ( L = 3) = P ( L = 4) = 1 / 5 (1) The robot has a camera that can be pointed to the left or to the right. In order to determine where it is, the robot tries to detect doors by looking either to the left or to the right (note that the robot faces east). As you can see in the figure, there are four doors in the hallway.
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