You wrote an algorithm that implements what's called Markov localization.

A second terminology for environments pertains to whether the environment is deterministic or stochastic.

The motions don't move at all, move right, move down, move down, and move right again.

So here is a quiz.

And it makes much more sense to talk about the probability or random variable equaling a value, or the probability that it is less than or greater than something or the probability that is has some property

Perhaps the probability of it being sunny is 0.7, probability of a raise is 0.01.

So how do I think about that?

You really don't want to wait for the truck to disappear.

It's not like the solution knows.

Narrator So, I'm going to ask you a tricky question and maybe you can calculate this.

So let me delete this.

What's the probability of Y?

In a deterministic action, it obviously succeeds, unless of course we run into a wall.

Specifically, what this routine should do is it should incorporate the probability of successful action and the collision costs.

Here is our sequence. There's a couple of sunny days 5 in total a rainy day, 3 sunny days, 2 rainy days.

You might say OK, that's the probably of getting exactly 1 times the probability of getting 2 out of 3 plus the probability of getting 3 out of 3.

As is easily seen, the 0.5 falls out, so we get 0.1 over 0.9 over a ninth, which is the answer for the first question.

Then the value of the state for the action go up would be obtained as follows.

So, here's another quiz.

1 if heads, 0 if tails

So Bayes' Theorem and let me do it in this corner up here.

Let's use the Laplacian smoother with K 1 to calculate the few interesting probabilities

So, this probability is equal to the product over all i of the probability of words of i given all the subsequent words. So that would be from word 1 up to word i 1.

At this point, our robot has localized itself.

Probability

Phil, the odds against

That means X equals 1 over 1.5, which is 2 3.

We asked them to estimate their likelihood of experiencing different terrible events in their lives.

We now apply Bayes rule.

And here is my answer. You can really read off the formula that I just gave you.

Here we had one probability to estimate.

What is going to happen to the Markov chain over here? What is that probability?

So the way that we would refer to this is the probability of both of these happening

This is called total probability.

Let's think about another one.

Let's do another example.

So we're not using this definition anymore.

Fixed zoom

What are the odds?

Thrun As usual, we can resolve this using Bayes' rule.

This one, this one, and one out here, and I put a little check marks underneath.

So with those two definitions out of the way,

Thrun So we're now ready to define Bayes networks in a more general way.

Y is always 0.6 probability so it must be that P(Y) is 0.6.

Now, I do have a quick quiz for you.