So Bayes' Theorem and let me do it in this corner up here. Bayes' Theorem tells us the probability of both a and b happening.

I think we're ready to substitute into the Bayes' formula, which we Bayes' Theorem that we rederived.

Bayes' rule tells you.

So before moving on, let's do a little bit of review of Bayes' Theorem, and I think that'll give us a good framework for the rest of this problem.

Pythagorean theorem.

Squeeze theorem.

Squeeze theorem.

Pythagorean theorem.

Pythagorean theorem.

Pythagorean theorem.

Monotonicity theorem.

There are two sources of information Bayes' rule tells you.

Bayes networks and examples of game theory everywhere I look.

You will never use ASA theorem or SAS theorem or anything

Pythagorean theorem again.

Some of the motivating examples included the Riemann Roch theorem and its generalization the Hirzebruch Riemann Roch theorem, and the Hirzebruch signature theorem.

Bayesian model comparison is a method of model selection based on Bayes factors.

And what Bayes showed was a mathematical way that you could do that.

Pythagorean theorem plus 1 squared.

That's just the Pythagorean theorem.

And that's the squeeze theorem.

So what's the squeeze theorem?

Then I've proved the theorem.

It's just the Pythagorean theorem.

And what's the binomial theorem?

And that's the Pythagorean theorem.

The classical results about interpolation of operators are the Riesz Thorin theorem and the Marcinkiewicz theorem.

The fundamental theorem of a field of mathematics is the theorem considered central to that field.

We're just doing the Pythagorean theorem.

Once again, just the Pythagorean Theorem.

We could use the Pythagorean theorem.

We just use the Pythagorean theorem.

This is just the Pythagorean theorem

So what is the binomial theorem?

Because once you understand what the squeeze theorem is, we can use the squeeze theorem to prove this.

The squeeze theorem is my favorite theorem in mathematics, possibly because it has the word squeeze in it.

So this is the mean value theorem.

What does the mean value theorem say?

So back to the mean value theorem.

That's all the mean value theorem is.

We can use the Pythagorean theorem here

He even taught me the Pythagorean theorem.

One student wrote, Now I'm seeing Bayes networks and examples of game theory everywhere I look.

So the convolution theorem well, actually, before I even go to the convolution theorem, let me define what a convolution is.

And what Bayes' rule says is, given my beliefs, the action should in some sense be optimal.