And that we say x and y are uncorrelated if correlation x and y are zero.

And sort of the more positively correlated they are,

the closer correlation core x comma y gets to one, and

the more negatively correlated as core xy gets goes to minus one.

And this is again, a description of a population quantity.

Not a sample quantity, right?

So this is a description, if you're using a joint probability mass function,

or a joint probability density function to model the population behavior of x and y,

then we want ways to summarize that joint mass function, or joint density function.

And the correlation is a summary of how related

joint random variables are from this distribution.

So it's a summary of a population quantity.

And of course if something is a population quantity we want

sample quantities that are able to estimate them.

So probably what you've heard of, if you've never had a mathematical statistics

class before, is the sample correlation.

And again the goal of the sample correlation is to estimate

the population correlation if you're using a probability model.

So the sample correlation estimates the population correlation.

So If you've ever had a sample correlation and you've had a probability model,

what you are trying to estimate is the population correlation.

The S demand is the population correlation.

So it follows the same rule we have so far for everything.

The sample variance estimates the population variance.

The sample standard deviation estimates the population standard deviation.

The sample median estimates the population median.

So all these sample quantities have analogous population quantities.