So, it's every thing we have been doing leading uptill now brings us to this point.

So we have to estimate that some way.

So the question is where did the 1.96 come from?

But this is really kind of one of the most important or interesting things about our universe, central

You had asked why did I drag you through all of these binomial distribution stuff and flipped so many coins, the reason is you're going to move now towards what's perhaps the most deep insight in all of statistics.

In another presentation, I'll give you the more formal mathematical, you know, the delta epsilon definition of a limit.

If it the most likely one will repeat itself and the further out you are, the less likely is to have a sample that it gets you this far out.

Just text us your temperature.

We'll learn more about this later, but the key thing to remember is we take many experiments, you add them up and outcomes a function just like this.

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We start out with the binomial distribution that you're familiar with from our last unit and then we move into the central limit theorem which basically means we've taken a number of coin flips to infinity.

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What you're about to see is perhaps the most interesting way to understand the central limit theorem and statistics of large numbers.

For large sample sizes N, the mean outcome of the sum of N independently drawn excised becomes more and more normal.

And you can't jump off a building and fly simply by believing you can. Just take my word for that one.

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Down to the point where they were undetectable.

And again you can see that the more luminous ellipticals seem to have shallower profiles.

So as x approaches one from the positive direction it looks like the limit of f... ...it looks like the limit of f(x) as x approaches one from the positive direction isn't zero It looks like it is one

So if x with a infinity would go to zero because it is a constant

Same thing, if instead of having a function here we had a constant

So you could have a situation like this, where you have a gap right over there and looks something

So if we have the limit as x approaches c of f(x) divided by g(x), this is the exact same thing as the limit of f(x) as x approaches c divided by the limit of g(x) as x approaches c which is going to be equal to

Because I could actually use some of that real estate.

So, to recap this, this piece, the most confusing part, is, we have variance, in the population, we have variance in the sample, and, we have variance, in this hypothetical distribution, of sample units.

So even for this different experiment with the die, we get about the same phenomenon that the sum of those seems to have a distinct high probability for what's the most likely outcome four and then it falls off in some interesting way.

Actually, let's deal with that right now.

A approaches infinity.

So plus 1 s.

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Thirty miles from the geographical centre of America, at its very heart, is the town of Grady.

So over here it equals zero

This is just another word, people might talk about the central limit theorem.

Well, lucky for us this is going to be equal to the limit of f(x) as x approaches c times the limit of g(x) as x approaches c

And I should say before I start this segment, I've taught statistics for a long time and I know that this last segment where we get to the probability histograms and central limit theorem is where a lot of students have trouble.

Welcome back.

Because obviously you can't evaluate infinity, but you could take the limit as something approaches infinity.

We call it a select opportunity .

It's a select opportunity. We have 32 shares...

I wrote a little bit bigger than I wanted to, but that's OK.

Stage magic relies almost wholly on the momentum error.

Heaven and hell exist in the hearts of man.

The sensations is that we have associated with blackout nearly always include the tunneling of the vision down to the central point where you just have light ahead of you.

Define our boundaries.

Now, should this state be an accepting state or not?