The probability of reaching S prime given that we started state S and apply action A.

We could have also done it other way.

Discount rate

Now what can we do ?

5 minus this 2.

So this is 8t squared plus I'm just dividing both sides of this equation by 2.

60 off.

Do you have a student fare?

These are 30 percent off.

Another way to kind of just talk about this is to get the present value of 110 a year from now, we discount the value by a discount rate.

Are there any discount tickets for me?

Are there special evening rates?

when the sale has a certain percentage ?

To compound the amount of money we invest we multiply the amount we invest times 1 plus the yield.

And it just depended on how the mathematics work out.

Free coupons. Discount Discount coupons.

Well, I don't give group rates, you know.

Perhaps only at a discount.

Let's say in every year it's going to make 1.

We could have said Let y equal the discount

Thirty percent off for USC alumni.

Yeah.

Well, that was x.

And this one that was in Kenya, they went around and distributed to people vouchers, discount vouchers.

Then to discount money in the future to the present, we divide it by 1 plus the discount rate so this is a 5 discount rate.

Well the antiderivative of y squared and you have to divide by 3, so it's y cubed over 6.

If I could get it for 90, that's a good deal for me.

So x minus twenty five percent x is equal to the sale price.

Get in deep. Deep deep deep deep!

So we seek to find the policy that maximizes the expression over here.

But what if I wanted to generalize a little bit ?

Be silent. Keep your forked tongue behind your teeth.

Special rates for state and federal employees.

Now this is really interesting, now we have a general way of calculating a discount for any given percentage off and any given product x.

You had your hat pulled down real strategically

This is the difference between the two.

It is our light, not our darkness, that most frightens us. You have to dig deep down.

I have some coupons I got last week.

So 2009 money, that's worth 1.

Let x be the price of the product I want to buy, the nondiscount price of the product in the store.

I'll say p, just so it makes sense, p is equal to the percentage off.

What is it about Superman?

In this example that I did in the previous video, it was the pre tax return on asset.

And this is scenario three.

Come on, boy! Deep. Get in deep.