The random variable x plus the random variable y.

Random variable y.

That's a random variable.

Or, since it's a random variable, the expected value of this random variable.

So that's our random variable.

let's say I have some third random variable that is defined as being the random variable x plus the random variable y.

So I have random variable x.

I have some other random variable.

The covariance of a random variable with itself is really just the variance of that random variable.

The population mean of random variable x.

Let's say we have another random variable.

That sample mean is a random variable.

This is for our random variable, x.

Let's say I have the random variable a, and I define random variable a to be x minus y.

I got four instances of this random variable.

It isn't true for any random variable, X.

And I'm going to define my random variable,

Now let's think about what the variance of random variable z is and what the variance of random variable a is.

So this is going to be equal to the variance of random variable x plus the variance of random variable y.

So let's say I have a random variable, X.

These are just specific instances of a random variable.

So this is the distribution of random variable x.

Let's do the same thing for random variable y.

But here, we're talking about y, random variable y.

And the random variable is just that function mapping.

So this is my definition of my random variable.

Let's define a random variable, X, like we always do.

Because now I'm going to define a new random variable.

So the expected value of a random variable, the expected value of a random variable is the exact same thing as the population mean.

But if you think about it, well, a random variable really is you can kind of view it as each instance of a random variable.

This is the mean of n observations of our random variable.

So it has some variance right here for random variable x.

And the x just means this is for random variable x.

A hundred instances of this random variable, average them, plot it.

I'll now introduce you to the concept of a random variable.