Dispersion of the normal distribution

You learned something really important.

Mean value of the normal distribution

Middle value in the normal distribution

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

Standard deviation of the normal distribution

So first let's revisit this normal distribution.

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

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

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

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

So, we're just looking at frequency on the y axis.

Value to which the standard normal distribution is calculated

The number for which the standard normal distribution is to be calculated

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

We already talked about this example earlier in class, but now it's in the content of normal distribution so let me take a second to show this to you.

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

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

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Then we know a lot about that distribution.

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.

It was, they were all over the place.

So we know the risks we're running for a type one error and a type two error, as researchers.

So a T distribution looks very similar to a normal distribution but it has fatter tails.

So, this script's end stands for normal, since Gaussian and normal distribution, they mean the same phase of synonymous and a

The number for which the integral value of standard normal distribution is to be calculated

With that said, let's play around a little bit with this normal distribution.

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

less fluctuation in those sample means. So then, if I plotted all my sample means.

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

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

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And D and E have 1 incoming arc that's shown over here.

This is one that's even wider than the two original Gaussians.

I mean, a distribution of scores in a sample on some variable.

I compute whether the measurement matches the color in the cell, in which case I call it a hit.

This distribution is also standardized into a Z distribution, which I'll get to in a minute.

look at everybody in the distribution.

Of 100. Now it's looking pretty close to the population.

Thrun So we're now ready to define Bayes networks in a more general way.

Here's a 2 dimensional space.

You can only have a finite number of values while the normal distribution is defined over the entire real number line.

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

This is from the counter table with very large interval here, so we can use a Gaussian approximation.