23 – 24 Limit Distribution Quiz V3

So, here’s a question for you that is somewhat involved, and I either want to check your intuition. Suppose we have five grid cells as before, with an initial distribution that assigns one to the first grid cell and zero to all of the other ones, let’s assume we do U equals one, which means with 0.8 chance in each action, we transition one to the right. With 0.1 chance, we don’t move at all and with 0.1 chance again, we skip and move two steps and again, let’s assume the world is cyclic. Every time I fall off on the right side, I find myself back on the left side. The question is, suppose I have an infinitely many motion steps then I actually get a what’s called the limit distribution. So what’s going to happen to my robot if it never senses but executes the action, one will go one to the right on our little cyclic environment forever? What will be the so-called limit or stationary distribution B in the very end?

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