Note that this is the same as figuring out the variance of 2 data points, 1 that's 0 and 1 that's 1.

In the example I've chosen here are the measurements of 5., 6., 7., 9., and 10.

Fused as one.

So we cross out row 3, column 2.

I find that amazing.

In particular, let's start with the variance.

Try it out.

Let me put commas here so it doesn't look like eleven.

The harder question is How often will an object come out of the pipeline being fed with objects?

Here it's obviously 1.

Here we're going to take 0, 1, 2, but we're going to add 1 to each, so 0 1 is 1, 1 1 is 2, 2 1 is 3.

Someone fouled me when I was shooting a 3 pointer.

sound . So, let's say here's my function.

So if I have 1 times 10 is clearly just equal to 10 1 times 10 to the negative 1

that's most of it. Here.

It may last for a minute, or an hour, or a day, or even a year.

So we cross out row 2, column 3.

Look familiar? 8 and 13 are both numbers in the 'Fibonacci series.'

If I say 21, what are all of the factors? Well, it's 1 and 21, and 3 and 7, and I think I've got all of them

But isn't this interesting?

The multiplicative identity is 1.

Let's think a little bit about what it means to multiply fractions.

If I were to take my original matrix, and I were to cross out this position's row and column.

What's 1 2 minus 3 2?

We start in the 1's place or you can even think of it as the 1's column.

Now, of temporary, set theta one equals one, what I want to do is figure out what is j of theta one, when theta one equals one.

Still not that great, but it will serve our purposes.

And over here, we have nine things with a mass of one kilogram, which we could write as 1 1 1 1 1 1 1 1 1.

But what if I wanted to say I guess we could call it the area between 0 and I'm trying to determine how general to be.

There's an x variable, y variable, and we have four data points.

We're going to start with 1, and we're going to go through each row and column at the same time, checking to see that that digit occurs once and only once in each row and column.

G of Z if Z is a real number is equal to one over one plus

That equals what?

This kernel applied in this location over here will give me a minus 1 times zero plus 1 times zero is zero.

And so five is five to the right of zero. Five is right over there.

So 5 is the same thing as 20 4, and then this plus 1 4 is the same thing as plus 1 4.

Let's go run it and see.

I'm just kind of reshowing you how I visualize when I cross out the rows and columns.

And in this situation, this would get you, well, one half, well, 1 times one half is just one half, times one half is 1 4th, times one half is 1 8th, times one half is 1 over 16.

Some people think that instead of starting by adding 1 1, you should start with 0 and 1.

Most school districts spend two thirds of that on payroll and overhead.

For the first data item, 1 the argument here would be 1 and the count will give me 1 because there's exactly 1 occurrence of 1.

So this is 1 times to the first 1 times to the 0 is equal to 1 times 1 which is equal to 1 1 times 10 to the negative 1 is equal to 1 10 which is equal to 0.1

Mornings look a lot better after nine hours of sleep. gt gt Pat

And it makes sense, right?