So, continuous variables do exist.

In addition, believe it or not, sometimes it's easier to think of

a variable as being continuous, than instead of having it discrete values.

Stock prices are certainly discrete.

We go in cents, or here in Switzerland in rappen.

Nevertheless, it's sometimes easier to model these random

processes with a continuous random variable.

So, continuous, that's really a tricky concept.

And now I want to spend the rest of this lecture thinking what is

continuous variable?

What does this really mean?

So, let's think of a random variable that can take on any real

number between zero and one.

And then I can ask a question, and let's start with a little in-class question.

What is the probability that this random variable will take on exactly

the number zero point, one, two, three, four, five, six, seven, eight, nine?

Think about this, what is this probability?

Before I give you the answer to this in-class question,

I want you to have a look at a little spreadsheet that I prepared.

Because Excel has this beautiful random variable function, RAND,

that allows us to simulate the random variable on zero, one.

Let's do that.

So, here now, I prepared a little spreadsheet for

you using the random number function in Excel.

Here, in every version of Excel, you have this beautiful function RAND().

This particular function gives you a random number between zero and one.

And so, now look at these numbers.

They are all different.

Now, what do you think is the chance I get a 0.123456789?

Let me try this again.

We have these random numbers, I click Enter, we get ten new numbers.

Look at this, they change all the time.

However, if you want to bet on a particular number, this is hopeless.

If you think there's any chance 0.5, 0.55 or from the in-class quiz question,

0.123456789 shows up, it's not going to happen.

Probability is zero.

As a little aside, for the techies among you, here in Excel,

of course, these are not truly random numbers.

They're limitations to the computer.

They're only so-called pseudorandom numbers.

And I only get a limited number of digits here,

so technically, we only have finitely many numbers.

However, this is meant as a representation of the true continuum.

And in that sense, the probability of every number is zero,

and we cannot hit any number that I give you ahead of time.

So, let's now wrap up this idea,

move back to the slides, and continue with continuous random variables.

There's really an infinite number of numbers between zero and one, and

we cannot count them.