And that's a key difference the binomial distribution is always finite.

If you have 10 patients, you might think of it as binomial distribution.

So obviously, in this binomial distribution, there are about 16 different outcomes from 0 to 15.

Normal Binomial

Displaystyle Binomial

Textstyle Binomial

AMS Binomial Expression

And we've factored our binomial.

This is the mystery binomial.

So just for our little Python program implementing the familiar expression of binomial distribution and with this program, I'll get the following.

So simple is the hypothesis testing and you use confidence intervals instead of, for example, the binomial distribution and that's really the common case.

And this is just multiplying a binomial.

This is the square of a binomial.

This is a square of a binomial.

Each of these is a binomial variable.

We factored it into two binomial expressions.

What is there to understand? Binomial theorem?

Distribution

Distribution

Distribution

What I've shown you in the beginning of class have from a coin flip to a binomial distribution all the way to a normal distribution, and you might think that this was challenging and indeed it was.

Then we graph the binomial just like before.

That's actually what I do in the other video, just to approximate the area under the curve and give you a good sense that the normal distribution is what the binomial distribution becomes essentially, if you have many trials.

Distribution Lists

Distribution List

T distribution.

T distribution.

T distribution.

And I encourage you to rewatch the video on probability density functions because it's a little bit of a transition going from the binomial distribution, which is discreet.

So this was a perfect square of a binomial.

This is a normal distribution, here's a cumulative distribution.

Choose Your Distribution

Select Distribution List

New Distribution List

Configure Distribution Lists

The distribution shows.

You're probably not used to factoring out an entire binomial.

left hand side into the perfect square of a binomial.

So a binomial is just a polynomial with two terms.

So let's say my binomial is Ax squared plus Bx.

So, this formula is the probability of what's call the binomial distribution and really was this is the accumulated outcome of many identical coin flips, and it leads us beautifully to our next lesson when we talk about very large experiments and the normal distribution.

I really want you to play with this and play with the formula and get an intuitive feeling for this, the cumulative distribution function and think a lot about how it relates to the binomial distribution and I cover that in the last video.

The distribution of the absolute least information is the uniform distribution.

The binomial distribution will say, what is the probability of getting a 5, and you just kind of look at that histogram or that bar chart and say oh, that's the probability.

What a bizarre distribution.