Finally the shape of this distribution of sample means will be approximately normal even if the distribution in the population isn't normal.

And, there's a standard deviation of the distribution of sample means, standard air.

Middle value in the normal distribution

little higher than if you do it, uh, orally. So we looked at this histogram before.

French translation

Here's the trick.

Concentrate all fire on their engines.

(Laughter)

And, again we don't know most, most of the time if the distribution in the population is normal.

And nobody minds that. We actively welcome it.

Let me ask the hard question now.

So first let's revisit this normal distribution.

We will be able to look at income distributions in completely new ways.

this is a word you'll see a lot in statistics books.

Could you enhance certain effects? Probably so.

So, Steven Spielberg, eat your heart out.

You don't do this for this relatively complicated expressions over here.

There's no way we've got enough powder to kill it.

They'll fluctuate, right.

Let's start with 2 Gaussians and say they have identical variances. Let's multiple them.

Don't have it, left my wallent in the car.

The way to think about this if there is K different cluster centers shown over here each one of those has a generic Gaussian attached.

This might be taxing my computer by taking the screen capture with it.

Suppose you're doing many experiments.

It's population based.

So a good measure of central tendency just describes the center point of a distribution.

So this is a cumulative distribution function for the same... for this

We have to look at the education of humans.

That means that if you sit at the left side of the distribution, and I'm looking at your neuropyschological abilities, the average person has moved to the middle or the right side of the distribution.

Suppose our mean is 10 and 13, and the variances are imbalanced 8 and 2 which corresponds to the following picture.

Dispersion of the normal distribution

Cows graze one day. They move, OK?

And I have to explain to you, the top of this graph shows you that frequency distribution that I talked about.

Then we have a Gaussian distribution that is centered around zero, because that's Mu.

My recommendation is if you have a multimodal distribution use particle filters if you can.

What we're going to do, is assume that the feature,

(Applause)

(Laughter)

Mean of the distribution

Your purse?

One being physically separate, but with a collective consciousness.

I finally want to teach you about the concept of a standard score.

Focus, focus! Plus fort, plus fort! Right, it's your turn.

To focus?

A positive times a positive contributes more to the sum.