0:00:00.000,0:00:06.000 Let's look at the measurement of this robot in its world with 5 different grid cells-- 0:00:06.000,0:00:09.000 x1 through x5. 0:00:09.000,0:00:16.000 Let's assume 2 of those cells are colored[br]red whereas the other three are green. 0:00:16.000,0:00:21.000 As before, we assign uniform probability to each cell of 0.2, 0:00:21.000,0:00:25.000 and our robot is now allowed to sense. 0:00:25.000,0:00:29.000 What it sees is a red color. 0:00:29.000,0:00:33.000 How will this affect my belief over different places? 0:00:33.000,0:00:36.000 Obviously, the one's for x2 and x3 should go up, 0:00:36.000,0:00:40.000 and the ones for x1, x4, and x5 should go down. 0:00:40.000,0:00:45.000 So I'm going to tell you how to incorporate this measurement into our belief 0:00:45.000,0:00:49.000 with a very simple rule--a product. 0:00:49.000,0:00:53.000 Any cell where the color is correct--any of the red cells-- 0:00:53.000,0:01:00.000 we multiply it with a relatively large number--say, 0.6. 0:01:00.000,0:01:05.000 That feels small, but as we will see later, it is actually a large number. 0:01:05.000,0:01:10.000 Whereas all the green cells will be [br]multiplied with 0.2. 0:01:10.000,0:01:16.000 If we look at the ratio of those, then it seems about 3 times as likely 0:01:16.000,0:01:19.000 to be in a red cell than it is to be in a green cell, 0:01:19.000,0:01:23.000 because 0.6 is 3 times larger than 0.2. 0:01:23.000,0:01:25.000 Now let's do the multiplication. 0:01:25.000,0:01:30.000 For each of those 5 cells, can you tell me what the result would be 0:01:30.000,0:01:34.000 multiplying in the measurement in the way I've stated. 0:01:34.000,0:01:38.151 Please, for these 5 boxes, fill out the number.