7 – 09 Probability After Sense V1

So, let’s look at the measurement of this robot in his world with five different grid cells x_1 to x_5. Let’s assume two of those cells are colored red, whereas the other three are green. As before, we assign uniform probability to each cell of 0.2, and our robot is now allowed to sense, and what it sees is a red color. How will this affect my belief over different places? Obviously, the ones for x_2 and x_3 should go up, and the ones for x_1, x_4, and x_5 should go down. So, I’m going to tell you how to incorporate this measurement into our belief with a very simple rule, a product. Any cell where the color is correct, any of the red cells, we multiply it with a relatively large number, say 0.6, that feels small but as we’ll see later is actually a large number. Whereas all the green cells will be multiplied with 0.2, we look at the ratio of those that it seems about three times as likely to be in the red cell than it is to be in the green cell, because 0.6 is three times larger than 0.2. Let us do the multiplication. For each of those five cells, can you tell me what the result would be multiplying in the measurement in the way I’ve stated. So, please for these five boxes, fill out the number.

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