expected values of minimums

[kryptic91]

Hey everyone, I recently started studying for the P exam and I've just started expected values. There's a question in the study guide about finding expected values of minimums that I don't really understand.

Q: The pdf of a loss is f(x)=0.5e^(-0.5x), x>0. An insurance will pay the entire loss up to a maximum of 1. Calculate the expected value of the payment.

The first step is:

E(X^1)=integral of [1-F(X)]dx from 0 to 1

Could someone please explain where this step came from? I'd appreciate it a lot.

[weezy]

Hey everyone, I recently started studying for the P exam and I've just started expected values. There's a question in the study guide about finding expected values of minimums that I don't really understand.

Q: The pdf of a loss is f(x)=0.5e^(-0.5x), x>0. An insurance will pay the entire loss up to a maximum of 1. Calculate the expected value of the payment.

The first step is:

E(X^1)=integral of [1-F(X)]dx from 0 to 1

Could someone please explain where this step came from? I'd appreciate it a lot.

It's the same as if you do it in pieces. Integrate xf(x) from 0-1 then 1f(x) from 1 to infinite. I like it better the long way, it's more intuitive.

[kryptic91]

It's the same as if you do it in pieces. Integrate xf(x) from 0-1 then 1f(x) from 1 to infinite. I like it better the long way, it's more intuitive.

In the picture that you linked, I found the integral of uf(x)dx from u to infinite to be u[F(infinite)-F(u)], but in the second step it says u[1-F(u)]. So could you explain why F(infinite)=1?

And sorry, but could you also explain how you went from the second step to the bottom step?

Thanks for the response

[NoMoreExams]

In the picture that you linked, I found the integral of uf(x)dx from u to infinite to be u[F(infinite)-F(u)], but in the second step it says u[1-F(u)]. So could you explain why F(infinite)=1?

And sorry, but could you also explain how you went from the second step to the bottom step?

Thanks for the response

Properties of CDF. Know these: http://en.wikipedia.org/wiki/Cumulat...ion#Properties

What he wrote is a bit math. incorrect, should be a limit but you get the picture.

[kryptic91]

Thanks, I get it now