Let me give you a final example in which I assume a uniform distribution, and I want you to fill in for me the distribution after motion.

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

So first let's revisit this normal distribution.

Dispersion of the normal distribution

Mean of the distribution

Your purse?

So, Steven Spielberg, eat your heart out.

I'm going to ask you now for the initial distribution that I'm writing up here, can you give me the distribution after the motion?

The plant ranges from the north of Europe to the south.

This tells you the height of the normal distribution function.

You put these 10 samples at once in the cage.

Here's my code. We have a loop for 1,000 steps.

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

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

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

An animal? An animal?

Let me ask the hard question now.

Linear middle of the distribution

Standard deviation of the distribution

Degrees of freedom for the t distribution

You learned something really important.

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

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

Now let me ask you a somewhat more challenging question.

The three main principles are what we just we worked through.

But in summary, we have a Gaussian over here, we have a Gaussian for the motion, with U as the mean and R square as its own motion uncertainty, and the resulting Gaussian in the prediction step just adds these 2 things up mu plus U and sigma square plus R square.

In addition to this, I will use a very simple p, that has a 1 at the second position and zeros elsewhere.

So what I'm going to do is show you the distribution of matter as a function of scales.

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

It's one standard deviation in the distribution of sample means. So this distribution of sample means, again.

Mean value of the normal distribution

Middle value in the normal distribution

Now, the reason why there is a minus sign is tricky.

Down here, I can normalize aux to have a total probability of 1, and then I return it.

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

I noticed that, yeah. Animals, mister, just animals.

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

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

And your new sigma square is your old sigma square plus a variance of the motion Gaussian.

0 density, 1 distribution

So I can get any value less than 20 given this distribution.

MV is the linear middle of the distribution.

STD is the standard deviation of the distribution.

Standard deviation of the normal distribution

That's largely influenced by the sample size.