And so to actually calculate this, what I do is I take the cumulative distribution function of this point and I subtract from that the cumulative distribution function of that point.

Cumulative 0 calculates the density function cumulative 1 calculates the distribution.

So what I did is I evaluated the cumulative distribution function at one to be right there.

a function has been defined called the cumuluative distribution function that is a useful tool for figuring out this area.

little bit, let me get out of pen tool so the cumulative distribution function is right over here then you say true when you make that Excel call.

K 0 calculates the density function K 1 calculates the distribution.

So what the cumulative distribution function is essentially let me call it the cumulative distribution function it's a function of x.

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

And that's because this value tells the probability that you're less.

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

So if I have... ...if I have the limit of

This might be taxing my computer by taking the screen capture with it.

But then to actually figure out the probability of that, what I do is I calculate the cumulative distribution function.

So if you wanted to graph this right here, you would say false in caps.

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.

Cumulated flag

One way, if you did want to memorize it, you said, OK, the integration by parts says if I take the integral of the derivative of one thing and then just a regular function of another, it equals the two functions times each other, minus the integral of the reverse.

You can equally define over states in action pairs.

This tells you the height of the normal distribution function.

And the way you get it is with the cumulative distribution function.

So what do we want to make our v prime?

Mu is the mean. Sigma squared is called the variance.

And that's what this is right here.

And then all of these, even though this may or may not have an exponent in it, it has the same type of symmetries as x raised to an odd power.

If f prime of t is equal to cosine of a t, what is a potential f of t?

BRDFs are just the start.

You remember this because that's what you programmed.

Starting with the following source code,

In Kalman filters the distribution is given by what's called a Gaussian.

So the important topics to take away from this segment.

If we take out the constants from inside of the integral, we get e to the minus sc times f of c times the integral from 0 to infinity of f of t minus c dt.

So this is derivative.

Well, we can do a little pattern matching here, right?

So you just learned about the concept of a probability density and that's very cool.

When I introduced you to the unit step function, I said, you know, this type of function, it's more exotic and a little unusual relative to what you've seen in just a traditional Calculus course, what you've seen in maybe your

So if a minus s is less than 0, and this is a negative number, e to the a minus s times well t, where t approaches infinity will be 0.

So when you take a derivative, when you take a partial with respect to just x, a pure function of just y would get

It's always good to use the exponential function, because that's easy to take the antiderivative of.

Well that's equal to what?

And way down here on the leaves are current research questions, which over here might be problems related to prime number distribution and over here some very specific work being done on randomized algorithms or hash functions, and way up here we might have new public key protocols

And we're going to see some concrete examples of taking a

Do not apply that here.

So how do we evaluate this integral?

Mean value of the standard logarithmic distribution

So, let's look at the luminous baryons first, those would be mostly in galaxies, and the way to do this is to integrate them spatially.