So it's the area from minus infinity to x of our probability density function.

So how do we study properties of clusters as a population?

And it makes much more sense to talk about the probability or random variable equaling a value, or the probability that it is less than or greater than something or the probability that is has some property

Let's think about another one.

Let's do another example.

So we're not using this definition anymore.

You know what the standard deviation means in general but this is the standard deviation of this distribution, which is a probability density function.

So what I'd like you to do is fill in these two functions.

Those values are discrete.

So is this a discrete or a continuous random variable?

What's the probability of the joint X, Y?

Einstein's wrong. Energy doesn't go mass times velocity light square in this dimension.

Question 1 In the first question, I'm going to ask you some very basic probability questions.

A probability theorist...

I'll even add it here just to make it really, really clear.

They are not discrete values.

You have discrete random variables, and you have continuous random variables.

We're talking about ones that can take on distinct values.

Similarly for tails, if you took a die

And I want to think together about whether you would classify them as discrete or continuous random variables.

Y is the mass of a random animal selected at the New Orleans zoo.

The exact, the precise time that you would see at the men's 100 meter dash.

So the important topics to take away from this segment.

The duration tells you about either their velocity dispersion or the individual masses, and the total number of lenses you see is telling you something about their density.

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

The same thing. A million to one we'd find it.

So, we actually just learned some interesting lessons.

Mass

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

Our age goes in for quantity regardless of quality.

What we're going to see in this video is that random variables come in two varieties.

So the number of ants born tomorrow in the universe.

So congratulations, you've implemented the very first example of probability where the event probability is 0.1 and the complementary event and negation of it is encapsulated in this function over here.

And if we wanted to know the mass of that cube, we would multiply the density function at that point times this dv.

And we find out that for the luminous mass alone, mass to light ratio doesn't change through the function of mass.

For those of you that know what a Gaussian random variable is or for those of you that know what a normal random variable is, you can also set W equals Rand N, one by three.

One is the super massive black holes and their nuclei and the other one is the dwarf family of galaxies.

It's just this nice, simple, expression