The simple correlation coefficient is about 0.9!

Well, this is my g of t, so g of tau is cosine of tau, cosine of tau d tau.

And when you would put tau in there, you get tau over 2 tau, and then minus minus tau over 2 tau, and then you get tau plus tau over 2 tau, that's 2 tau over 2 tau, which is equal to 1.

So cosine of t times sine of tau times the cosine of tau d tau.

These are called tau tau.

1 over 2 tau when t is less then tau and greater than minus tau.

So this is equal to the integral from 0 to t, of sine of t, times the cosine squared of tau d tau minus the integral from 0 to t of cosine of t times sine of tau cosine of tau d tau.

So 1 plus cosine of 2 tau and all of that is d tau.

Vung Tau

So this is minus tau, and this is plus tau.

You have one tau here and then another tau there.

So it's is going to be sine of t minus tau times g of tau.

If we said u is equal to sine of tau, then du d tau is equal to the cosine of tau, just the derivative of sine.

It was sine of tau.

Or we could write that du is equal to the cosine of tau d tau.

So this is equal to sine of t times the integral from 0 to t of cosine squared of tau d tau and then minus cosine of t that's just a constant I'm bringing it out times the integral from 0 to t of sine of tau cosine of tau d tau.

So what is the limit as tau approaches zero of my little d sub tau function?

This is tau is equal to 0 to tau is equal to t.

If my new tau is going to be here, let's say my new tau is going to be there, I'm just going to pick up my new tau there, then my 1 over 2 tau, the tau is now a smaller number.

And that would be equal to the integral from 0 to t, of e to the minus t minus tau, sine of t, minus tau, times sine of alpha tau, dtau.

I could write this as sine of ? out ? t minus tau, times alpha I'm taking the sine of all of those things times e to the minus tau, sine of tau, dtau.

Correlation

Ba Ria Vung Tau

Oh, sorry, d tau.

So let me rewrite that sine of t minus tau, and we'll just use the trig identity, that the sine of t minus tau is just equal to the sine of t times the cosine of tau minus the sine of tau times the cosine of t.

So I'm going to write the sine of t times the cosine of tau minus the sine of tau times the cosine of t, and then all of that's times the cosine of tau.

I mean, I could rewrite this integral as the integral from minus tau to tau and we don't care if infinity and minus infinity or positive infinity, because there's no area under any of those points of 1 over 2 tau d tau.

I'm just distributing this cosine of tau.

Coefficient.

last video in the playlist, I showed that the cosine squared of tau I'm just using tau as an example is equal to 1 2 times 1 plus the cosine of 2 tau.

The base is 2 tau.

Just to give you a sense of the correlation, the correlation is about .5.

You could get this is going to be equal to you take the antiderivative of 1 over 2 tau, you get I'll do this just to satiate your curiosity t over 2 tau, and you have to evaluate this from minus tau to tau.

Real coefficient

Imaginary coefficient

leading coefficient.

And notice this coefficient is the same as that coefficient.

We're integrating with respect to tau.

Sorry, 1 over 2 tau dt.

TNEF Correlation Key

The leading coefficient of the first row is 1 2 is the leading coefficient of the second row 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient.

I have to be careful with my taus and t's, and let's see, t and tau, tau and t.

By the inverse of the coefficient.

3 The Gini coefficient (coefficient of income concentration) makes it possible to numerically assess the degree of inequality.

It's going to be 1 2 sine of 2 tau.