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

There's a Markov chain over here with two states.

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

In this video, I'd like to talk about the Gaussian distribution, which is also called the normal distribution.

In Kalman filters the distribution is given by what's called a Gaussian.

Such a representation of probability over spaces is called a histogram in that it divides the continuous space into a finite many grid cells and approximates the posterior distribution by a histogram over the original distribution.

And so therefore, their kinetic energy can be characterized by a velocity dispersion.

If I were to measure where the peak of the new Gaussian is, this would be a very narrow and skinny Gaussian.

Thus, I suspect that each of these examples was distributed according to a normal distribution or

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

So first let's revisit this normal distribution.

Let me ask the hard question now.

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

Dispersion of the normal distribution

Then that corresponds to a

Mean of the distribution

Your purse?

Putting it in population parameters, but putting it in sample statistics.

There's a 95 chance that the true population mean, which is the same thing as the mean of the sampling distribution of the sample mean, there's a 95 chance, or that we are confident that there's a 95 chance, that it will fall in this interval.

Look at the new locations. Texas,

This tells you the height of the normal distribution function.

0 density, 1 distribution

If you remember from lecture two when we started to talk about probability, we can use the normal distribution.

What I want to do in this video is to generalize it.

And this is the world your children will live in.

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

T distribution right over here.

At that point you should have, statistically at least, a good separation between true distribution in space and the peculiar velocity distribution.

So, Steven Spielberg, eat your heart out.

Linear middle of the distribution

Standard deviation of the distribution

Degrees of freedom for the t distribution

You learned something really important.

Here's a 2 dimensional space.

Intuitively speaking, this is the case because we actually gain information.

So let me draw a

And I'm just showing this to you again because it's so nice.

And, the correct answer here is 0. Any specific continuous thing, 0.

But if you're not sure or if it's been a while since you've worked with a Gaussian distribution or the normal distribution then please do watch this video all the way to the end.

You assume first that galaxies are where they're observed velocities imply.

Mean value of the normal distribution

Middle value in the normal distribution

Let me make it very clear.

Each place had a probability of 0.2.

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