Minus 2b looks like this.

Now I'm going to say that these are position vectors, that we draw them in standard form.

Oppenheimer, Heisenberg, Fermi, and Teller.

That's my vector x.

Let's just say that my vector is the vector 2, 1.

So let's just start at some arbitrary point.

I just can't do it.

That's the vector in standard position.

The other possibility (Laughter) is, perhaps, Enrico Fermi himself was an alien.

So this is vector a in standard position right there.

Now what would be a graphical representation of this set?

Since when did a baroness outrank a countess?

(Laughter)

like that and I would go back 1 and then up 2.

Let's say that it is equal to 1, 2.

That's it.

I've done this before.

How soon can your team be ready?

So I go to the right 2 and I go up 3.

If I do 2 times our vector, I'm going to get the vector 4, 2.

This is going to be this blue line.

So b minus a looks like that.

Named after the scientist Enrico Fermi.

That's a.

Germany, my own country, in the year 2000, featured in the lower quadrant, below average performance, large social disparities.

Fermi problems are named after the physicist Enrico Fermi, who's famous for making rapid order of magnitude estimations, or rapid estimations, with seemingly little available data.

But why don't we see any evidence of it?

And yet, to the best of our knowledge, we are alone.

Our vector x was 2, 4.

This is a set of vectors right here, and all of these vectors are going to point they're essentially going to point to something when I draw them in standard form, if I draw them in standard form they're going to point to a point on that blue line.

And let me define vector y to be minus 4, minus 2.

If I were to do minus 10, I would get a vector going in this direction that goes way like that.

But the convention is to often put them in what's called the standard position.

Next roll the cotton in some Vaseline

But I think this collinearity of it makes more sense to you if you say, oh, let's draw them all in standard form.

This confused his colleagues, obviously, because they were sitting right there with him.

Where is everybody? asked Fermi, and his colleagues had no answer.

And the idea is that everything is defined.

Okay, so sum of squares, mean squares, that gives us variance.

Standard position is just to start the vectors at 0, 0 and then draw them.

And then vector b in standard position is 3, go to the 3 right and then up 1.

And at first when you look at it, this vector right here is the vector a plus b in standard position.

So this we rewrite as (let me use that same green color) 373 plus... we want to write the ones under the ones place, and the tens place under the tens place, so that we're adding the appropriate values.

So to wrap up here, the, the tools that we need for, for inferential statistics are the normal distribution, knowing its properties.

Let's say we have the vector a, which I'll define as let me just says it's 2, 1.