A robot can either be in one of two locations: L_1 (which does not have a window) or L_2 (which has a window). The robot doesn't know exactly where it is and it represents this uncertainty by keeping track of two probabilities: P(L_1) and P(L_2). Based on all past observations, the robot thinks that there is a 0.63 probability it is in L_1 and a 0.37 probability that it is in L_2. The robot has a single camera. The robot observes observes a window through its camera, and although there is only a window in L_2, it can't conclude with certainty that it is in fact in L_2, since its image recognition algorithm is not perfect. The probability of observing a window given there is no window at its location is 0.1, and the probability of observing a window given there is a window is 0.95. After incorporating the observation of a window, what are the robot's new probabilities for being in L_1? Report your answer to 3 decimal places.
A robot can either be in one of two locations: L_1 (which does not have a window) or L_2 (which has a window). The robot doesn't know exactly where it is and it represents this uncertainty by keeping track of two probabilities: P(L_1) and P(L_2). Based on all past observations, the robot thinks that there is a 0.63
The robot has a single camera. The robot observes observes a window through its camera, and although there is only a window in L_2, it can't conclude with certainty that it is in fact in L_2, since its image recognition algorithm is not perfect.
The probability of observing a window given there is no window at its location is 0.1, and the probability of observing a window given there is a window is 0.95. After incorporating the observation of a window, what are the robot's new probabilities for being in L_1? Report your answer to 3 decimal places.
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