And if you look at the data, when you have that kind of a structure, you get a very even distribution of the shops and the physicians and the pharmacies and the cafes in Paris.

So there's about 86 billion neurons in our brain.

Mean of the distribution

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

You can see areas where neuronal cell bodies are being stained.

Linear middle of the distribution

Here's a quiz for you.

Mean value of the normal distribution

Suppose I use the following Gaussians μ 10, σ 2 4, ν 12, r 2 4

Here is an example of a particular cluster, where different contours show, say, average distribution of galaxy light, or the number density, or the inferred galaxy mass, or mass distribution for the whole cluster.

That's largely influenced by the sample size.

MV is the linear middle of the distribution.

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

I'm giving you a skeleton program, which has a function update, that takes as an input a mean and a variance for the first distribution and a mean and a variance for the second distribution and outputs the new mean and the new variance of the product of those.

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

Cutting a cake into equal pieces is rather difficult.

Mean value of the standard logarithmic distribution

That's called a probability histogram.

A 2 dimensional gaussian is defined over that space, and it's possible to draw the contour lines of the gaussian.

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

At the end of the month we count your clicks

Here, I said samples equal to 30 or greater, some people would be a little more liberal then that and say if you have samples of even twenty or greater you'll get a normal distribution.

The mean of this gaussian is this x0, y0 pair, and the co variance now defines the spread of the gaussian as indicated by these contour lines.

I've got in my example minus the mean, minus the center, minus the mean of distribution.

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

And you have to imagine doing that squeezing without any imperfections, without any little spots where there were a few more atoms than somewhere else.

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

They'll fluctuate, right.

Can I change the order and always get the same result?

But now we'll look at histograms that represent distributions of samples.

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

The prior has a mean of mu and a variance of sigma squared.

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

How did we keep track of time without a clock?

This is one possible, events in which a is true divided by well, let's say, equally probable.

So, you can get into the more interesting version of state spaces, but we're not confined to unimodal distributions.

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.

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.

It makes no sense to call this unipolar or multi polar.

Or another way to say this is 3 5 or three fifths

And that's best depicted by this diagram over here.

Suppose you're localizing another vehicle, and you have a prior distribution that looks as follows.

I don't have time to do repeated samples. But I rely upon this idea of repeated samples to do my inferential statistics.

And we said at 1.70, people are willing to eat two million cupcakes in a year.

I just took an a and I distributed it along this whole sum.