This is going to be, this term right over here is going to be p squared minus p to the third.

So the percentage of variance explained is exactly the same.

It will change that value to the new exclamation point.

Now I have an assignment that introduces the new variable q and assigns p to that variable.

P of happiness given S and R times P of S and R, which is of course the product of those 2 because they are independent, plus P of happiness given not S R, probability of not as R plus P of H given S and not R times the probability of P of S and not R plus the last case,

We know that p is a pointer to a list let's say it's 1, 2, and 3.

And that's called a mixed strategy.

You might remember for P 0.5 then you go to the truth table, you'll find the answer is 0.375.

So all you're going to modify is the 1 p into something that if I give a probability p returns to me the probability of seeing heads twice in this coin that is the probability of heads.

Then we do the assignment.

Suppose we introduce the variable q.

So let's look at what happens in the Python interpreter.

And then this term over here, this whole thing over here, is going to be plus p times 1 is p. p times negative 2p is negative 2p squared.

In this first procedure, there's only one line.

Once again, based on this P, I'm going to start bringing in rules 1 and 2.

The mean, the expected value of this distribution, is p.

Well, we calculate this P value based on where it falls, given the assumptions.

And that puts you out in the extremes of the T distribution or that Z distribution.

This is 2P 3 P.

Let's look at the measurement side, and suppose we wish to know the probability of an internal state variable given a specific measurement, and that by Bayes rule becomes P of Z1 given X1 times P of X1 over P of Z1.

We can factor P of H given R as P of H given R and S, sunny, times probability of sunny plus P of H given R and not sunny times the probability of not sunny.

We multiply the p value as before for the exact set off by pExact.

So the top line here says the P value that you see.

Given that the null hypothesis is true.

So, E would announce that strategy for some number P.

We could observe a correlation.

So, in the final step of the particle filter algorithm, we just have to sample particles from P with a probability that is proportional to its corresponding W value.

And i has the value of 0.

Formally, we define a probability function to be P(X), and it's a value that is bounded below and above by 0 and 1.

Well, remember that the P value that we get, as I just showed you from the normal distribution.

So as the first exercise, say this is the probability, let's print the probability of the inverse event.

This should look familiar.

We're going to introduce the auxiliary variable s, which we build up in three different steps.

Now we have an assignment that stores in the value at position 0 of p the letter y.

Whereas the joint distribution over any 5 variables requires 2 to the 5 minus 1, which is 31 probability values, the Bayes network over here only requires 10 such values.

Then we use append, passing in 3 as the value to append, invoking append on the variable P, and then we have an assignment that assigns the P the result of P the list 4, 5.

And if you want to factor a p out of this, this is going to be equal to p times, if you take p divided p you get a 1, p square divided by p is p.

So that cancels out.

So this is going to be equal to 1 minus p.

So pretty straightforward.

Now let's add that pink p to both sides of this equation.

Well that's just the probability weighted sum of the values that this could take on.

It's that grammar of balanced parentheses.

Another way to think about that is let's say that we're in a particular state like this one

And the sentences are P or not P, P and not P,