Those values are discrete.

You have discrete random variables, and you have 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.

It could be 9.58. We can actually list them. So in this case, when we round it to the nearest hundredth, we can actually list of values.

This is the first value it can take on, this is the second value that it can take on.

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

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

Anyway, I'll let you go there.

Most of the times that you're dealing with, as in the case right here, a discrete random variable let me make it clear this one over here is also a discreet random variable.

It's 0 if my fair coin is tails.

That's my random variable Z. Is this a discrete random variable or a continuous random variable?

While continuous and I guess just another definition for the word discrete in the English language would be polite, or not obnoxious, or kind of subtle.

Once again, you can count the values it can take on.

Let's think about another one.

Let's do another example.

So we're not using this definition anymore.

There's no way for you to list them.

So is this a discrete or a continuous random variable?

They are not discrete values.

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

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

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

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

So the number of ants born tomorrow in the universe.

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.

But if you can list the values that it could take on, then you're dealing with a discrete random variable.

So, we actually just learned some interesting lessons.

Well let's define one right over here so I'm gonna define random variable capital X and they tend to be denoted by capital letters so random variable capital X, I will define it as is going to be equal to 1 if my fair coin rolls heads and it's going to be equal to 0 if tails

Let's think about let's say that random variable Y, instead of it being this, let's say it's the year that a random student in the class was born.

let's look at some actual random variable definitions.

It's 1 if my fair coin is heads.

And if you want it to write, and then you would try to figure it out somehow if you had some information

And discrete random variables, these are essentially random variables that can take on distinct or separate values.

The exact precise time could be any value in an interval.

Now what would be the case, instead of saying the exact winning time, if instead I defined X to be the winning time of the men's 100 meter dash at the 2016 Olympics rounded to the nearest hundredth?

The probability of any random variable Y can be written as probability of Y given that some other random variable X assumes value i times probability of X equals i, sums over all possible outcomes i for the (inaudible) variable X.

What's the probability of the complement?

At some level there are a couple differences in methods.

So let me delete this.

What I want to discuss a little bit in this video

And we know that our variance is essentially the probability of success times the probability of failure.

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

In this case, remember we had a set of random variables X1 up to Xn.

In the next video, we'll continue this discussion and we'll take a little bit about the types of random variables you can have.